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I edited the question significantly because it didn't make sense as written, but I strongly suspect it is correct in its present form.The requirements on a function that allow it to be a density are that it is everywhere non-negative and that it integrates to one over the set of reals.The anti-derivative of your function is the product of k and the arctangent of x. Evaluating this over the real line gives the product of k and pi. The only value of k for which this product yields one is the reciprocal of pi.

While I certainly agree with those who think (nay, "believe" may be a better word for some tech evangelists) the new tech reading devices are more convenient, I am agnostic with respect to their essential VALUE and critical of the outsized impact of their negative aspects.Firstly, let me tell you about me, then I will give my list of pros and cons.I am a tech-savvy educator. I was always the first in my school district to implement new technologies into my teaching and lessons. Only once, when a teacher beat me to the punch in using hand-held quizzing devices, has anyone in my district ever had something before I had already been "piloting" it in my classroom (high school & college biological sciences and environmental sciences).I personally own 2 Kindles, 3 iPads, 3 versions of the iPhone, multiple Mac & PC computers (Mac much preferred) with Mac OS9, OSX, WinXp, Win7, and a couple flavors of LINUX, several "off-brand" reading/text devices that never survived in the marketplace, graphing calculators, and other gadgets that have come and gone with the tide of fashion. ThereIn the classroom:I installed my own wireless network so students could bring their own devices and share data, files, and bandwidth with me,I used LCD screens and an overhead to project computer screens, then LED projectors, then digital computer projectors, then a blend of digital projectors and electronic whiteboard (SMART) with tablet-sized controllers, digital ink pads (Qomo), and drawing tablets (WACOM)I used digital data acquisition software and hardware (i.e. "probeware") from Vernier and PascoI set up a special GoogleDocs (before GoogleDrive was the name) account before Google made educational accounts available, had a classroom DropBox account, and used electronic distribution of reading materials and submissions of homework possible.My classes used physical texts, electronic texts (minimal, since the cost was prohibitive) and digital copies (PDF) of many, many articles from newspapers (especially NYTimes Science Tuesdays), popular science journals, and some professional science journals.Now, as I say, I am no enemy of technology and readily embrace it for my own use and in my own learning. As a skilled adult learner, I know which media best suits my preferences and proclivities as I seek to come to understand new concepts and experience new ideas.However, my students generally did not and do not have these metacognitive skills, nor have they developed or owned the disciplines needed to be able to evaluate their own learning much beyond the ability to predict whether they might pass today's quiz.Because of that issue: the lack of student self-awareness of learning and metacognition and their general lack of "expert learner" discipline, I rarely relied on electronic devices to provide significant amounts of information, but rather used them as tools for data acquisition and then tools for analyzing, displaying, and discussing the data. Most "big" information on major course concepts came from reading the physical text and re-interpretation and extension by me, as the teacher, and in group discussions. Ancillary information, current events (involving the concepts), and relevant examples of the concept came through guided readings of articles (sources mentioned earlier) and self-directed "research" of information via the Web with general guidelines and suggested search topics provided.25+ years of classroom teaching showed me that my students were just like those used in many studies of how student approach different text media. They essentially "scanned" or "skimmed" electronic media and interacted more deeply with physically printed text--if they read anything at all. Simply making the lessons more "tech-oriented" pleased the students for the first lesson or so, but once they realized they still had to develop the skills to learn the material and to integrate it into what they already knew, they came to find the new tech gadgets (first, a limited number of shared desktop computers, then a lab set of laptops, then multiple lab sets of notebook computers, and eventually individual student "netbooks") as just another "text book." The newness wore off in days. Retention of electronic media readings was lower than that of reading the physical text. I even ported my Bio-1 text to an electronic form (PDF) and assigned the same chapters. Kids just "skimmed" the electronic forms --just as they had been taught to do by the design and implementation of the billions of World Wide Web pages!So, I ask this: For k-12 students in the USA, is it any more convenient for them to own electronic copies of their textbooks on a single device (say, a Kindle or iPad) if they are NOT going to read the texts or are only going to skim them anyway?I say no.Because of the way that publishing companies have expertly set themselves up as the arbiters of curriculum in the USA, by virtue of also being the ones who oversee the writing of many of the the US States' End of Course Assessments (ECA) and of the entire Common Core (CCSS) Assessments, they effectively control what is included the textbooks and can demand whatever they want for remuneration. In my state, at least (IN), the cost of the intro biology text is as much as 6 times the cost of the same physically printed textbook. There is NO cost incentive in the long-term. There is usually an insignificant savings in the short-term.Now to other matters more practical and immediate to the teacher and student.As someone already has stated, no textbook has ever run out of power, had a dead battery, or required a special adapter for its use. ALL of these happen -- and in any school, they happen every day! This issue has an impact on the student, the teacher, classmates, and the IT department. It steals time and other precious resources (people and educational $$). The lower the grade level, the more the teacher will have to intervene--and disrupt their lesson flow and classroom time management. It is largely a non-issue with physical textbooks.If someone "forgets" their single reading device, or it is lost, stolen, damaged, or otherwise incapacitated through an Act of God (I had a student say: "My dog ate my netbook"!), ALL of their customized material is out for the day. Some of my students took advantage of this loophole in technology curation and "forgot" their netbooks regularly. Since their netbook was personalized for their set of classes before school had started, a simple "loaner" netbook would not d0--unless it had everything in every course that any student might possibly be taking that semester. Our IT folks couldn't/wouldn't do that, so "forgetful" students, or students who suffered a loss, often missed a day or more of lessons until something could be specifically set up for them. In addition, the number of loaner netbooks was necessarily small due to expense and maintenance. The number of spare computers also shrank throughout the year as loaners were brought into full-time service to replace broken, lost, or stolen computers. These are not a trivial issue in a typical school with more than 100 students. ...And Yes, Our students were on the hook to pay for lost, broken, and stolen computers. They were offered insurance at the beginning of the year at a nominal cost. This factor did not improve results. What happened is that more than a few students had parents that simply refused to pay up when their child lost or broke a computer and in the inimitable wisdom of the admin & IT folks, that student was no longer allowed to have a computer (until the parents paid the bill).The reliance primarily on keyboard input removes a thought-flowing physical act we know as handwriting. We know from research that marking up a paper with a pen & highlighter does something different in the brain than performing the same acts with a keyboard (Kindle) or even with a stylus (iPad or Tablet). While we are not yet sure of the longer-term consequences, we know that physically marking a physical text results in better memory (immediate, short-term, and for several days) of the process and the reasoning behind the markings than the electronic form of marking.Do I find "pros" with tech gadgets in the classroom?When they are used for things that only the tech gadgets can do better than previous technologies and can aid the teacher in helping the students gain knowledge, analytic skills, and to develop better self-awareness of their own learning.To that end, using an iPad as a simple reading device is, I think, a mistake. Using it to collect, display, and aid in analysis of data is a wonderful use! Using the iPad, then, to write a communication to explain what the student did and why they did it increases its usefulness. THEN--using it to browse the web to find an article in a journal that supports the student's conclusions and constructing a presentation (individual or group) that reviews the article as it applies to the recent student work has very good value.As a way to re-do worksheets and make them more "appy," or to be the receptacle of the textbook...>>Phhbbbbbbttt!!<<(For those who do not recognize that last outburst - it is a "raspberry" and a display of derision.)There is more that can be said, but I bow to the constraints of time and Quoran space.

No, you can’t be sure of increase in marks. In fact, in the revaluation form it is written that YOU HAVE TO FOREGO YOUR CURRENT RESULT AND ACCEPT WHATEVER YOU GOT WHICH COULD RESULT IN INCREASE, DECREASE or SAME (NO CHANGE). ”Read full answer”And that means you are not going to get the best of two marks. You might be having 6–7 points in exams and you might have wanted to stretch that up to 8–9 points. But if you fail at doing so then your new marks will be Zero (if failed) or 4–5 (if decrease) instead of your 6– 7 (same). Got it !!!REVALUATION PROCESS OF DELHI UNIVERSITY IS HORRIBLE.COVID-19 Revaluation NoticeRead and understand this notice thoroughly before you proceed for revaluation.http://www.du.ac.in/du/uploads/Examination/10052020_Revaluation-Notification.pdfThis is going to be a long answer (Approx 10 mins read), but it is going to resolve most of your queries.You have three options or more depending upon the situation you are in :1.Rechecking : Rs 700 It means they will just count the marks, summing up marks or better say Re-Totaling.2.Revaluation : Rs 1000 it means they will check your answer sheet again. Three invigilators.3.Copy of your answer sheet : Rs 1200-1500 That’s exorbitant amount.Please verify the fees on your own. They might have updated after 2018.Don’t go for Rechecking. That is of No Use. Copy of transcript is needed in the case you might be failing for 2 years and not able to clear your exams after all of your efforts or you might want to challenge Delhi University in court.Coming to Revaluation process :Revaluation process of Delhi University is horrible. Not worth your money i.e, Rs 1000 for each paper. This will not ensure your increment of marks. If you are failing in some paper in 3rd-year result, then absolutely go for it. Otherwise, don't take any risk. I have learned that DU revaluation paper is checked by low standard teachers who don't care about the future of a student. Their one little mistake can cost a student his reputation, one whole year and no further admission in PG and no general competition exams.Let's start with some statistics, in the year 2017 May Exam, around 1425 students have applied for Revaluation of 3rd-year paper and out of that approx 850 students have been passed. You see the rate approx 60% of the students have been passed. Does that mean they have been failed deliberately or due to ignorance or negligence? It seems like they have made a revenue model out of this.Delhi University earns over Rs 3 crore in revaluation fees, rechecking answer scriptsDip in English Honours' Grades Across Delhi University, Students Cry Foul Play - DU EXPRESSLet's come to process for applying revaluation :First, you have to apply for revaluation within 15 days of the date of declaration of result and that too offline. You need these things :Your admit card,Your Marksheet,your College ID card,Revaluation form and a copy of Fee Receipt (take note of transaction id or payment reference number).After you got all these documents. Check your college administration whether exam related concerns are under South campus or North campus. In my case, I have gone to the North campus. Go to Viswavidyalaya Metro station Gate no 1/2. Take E-Risckshaw to Reach Delhi University Main campus Gate no. 1, Upon entering take the first left cut. Go to window no 2. Submit all these documents and Hope for the best.You will be paying online but submitting your documents offline. I don't know how students outside of Delhi NCR would have felt when they have to come from distant places and just to submit 4 sheets. It would have cost them at least Rs 2000 for not-so-sure-result. In the revaluation form, you will be signing and giving your consent that you have to forego the current result and accept your re-evaluated result no matter what. The fee Rs 1000 for one paper is exorbitant compared to other universities.Here goes my story (similar to yours) :I have experienced this. At present, I am pursuing Post Graduation in Statistics.I have been enrolled in BSc Math(H) in Rajdhani College of Delhi University in 2015–18. I had 8 SGPA in 5th semester and I was expecting 7 SGPA in 6th semester along with an improvement paper (Riemann Integration) of the 4th semester. I had obtained 5/10 Grade points in the paper of Riemann Integration in 4th semester. So I had taken improvement exam in the 6th semester with the intent of making it to 7/10 and spent Rs 400 for the same.But when the results are declared on 10 July 2018 for the last year 6th semester. My hopes are shattered. I had been failed miserably in 4th-semester improvement paper and obtained just 4/10 Grade points in the 6th-semester paper in which I am very confident of scoring at least 8/10.So I decided to go for the revaluation process. I spent Rs 2000 for two papers revaluation fees. Even the results are declared very late approx 2 and a half months but I was unable to take admission for Post Graduation. I got 4/10 in both papers in which I have opted for revaluation. 4/10 is passing criteria and avoiding the embarrassment of failing.My result were out in the last week of September i.e, almost 2 months (10 July - 28 September) after the declaration of graduation results. They will also send you result in an envelope within 10 days of declaration of results on your address. In the mean time, you can check and download the result from the official website.University of Delhi | ExaminationAbove link contains the list of Revised/No change results since 2016. If you are gonna apply for revaluation. Then your result will be declared here. You have to download both pdf corresponding to your year and session. Then you need to look for your name in those pdfs.Revised ResultsNo Change ResultAlthough I have managed to secure First division with a score of 6.784 CGPA But that was not worth my time, money and effort. I would have obtained more than these marks without going through this tedious procedure and mental trauma.In the end, I will say I just wasted my Rs 2400 for less than expected marks. I should have opted for not taking the improvement exam. Don't depend on revaluation procedure and better prepare your papers prior to exams.Now I am planning to file a case against Delhi University Exam department. Let's see how the matter will unfold in the court. Time to fight back and being possibilist.Edit 1:Students are asking me How to pay the fee? Search on Google “dumisconlinefee”. Check and verify that link because when I was filling the form the link was different. Now they seem to have updated the website.Misc FeeClick on the above link “Fee”This link will redirect you to register yourself for Misc fee.Click on the first link. Get registered by filling your details. Obtain the ID and password. Use that to login. Click on the dashboard. Proceed to pay for your revaluation of transcripts. Print out and save a copy in your email.STAGE 1STAGE 2STAGE 3Lemme tell you, you will not receive any confirmation/acknowledgement mail of these all. Keep all your documents, screenshots, fee receipts for future reference.STAGE 4Fill your form PROPERLY & also get it verified/match with your teacher or classmates.That 4/5 means whatever points you got like 4 ( grade points obtained ) & 10 or 0 & 10 (if failed).5. Annual/Supp./Sem/Year means your present semester.Same goes for6. Part I/II/III Your present yearThey will verify this all anyway. From the column DATE OF EXAM TAKEN they will know. They have your full database. Don't worry much about it.You need admit card of the last exam you had taken. If you don’t have admit card. No problem, you can get a copy of the same from your college exam department. You need to write an application for the same addressed to Dean of your college. Subject you can write NEED COPY OF ADMIT CARD FOR APPLYING REVALUATION. Support staff will provide you a duplicate admit card. This whole procedure will take at most half an hour in your college. Do remember that administrative department of North and South campus close by 3 PM.Edit 2: Here I am uploading the copy of result before and after Revaluation.These images are just for showing what it comes written on the result :1st image If you fail.After Revaluation2nd image If your paper is cleared in revaluation. ( Notice the text in blue link) That's it.This is what comes written on the result. It exactly has the SAME VALUE as your regular result. For any more queries, You can contact me on 8860106115 https://www.facebook.com/aarunkv98 but first drop a WhatsApp msg describing your brief introduction, concern & problem in a single long message. Like this :Your name :Your college :Your Correspondence :Your graduation subject :Revaluation subject :Your current CGPA :Then your problem or concernPlease don't send me thread of messagesIf you will not get reply within 2 days, then ring me up anytime 🤝. I have been contacted by approx 100 students since I have written this answer. Don’t feel hesitant to talk about it. You are not first and neither you are going to be last. Fight a little harder. Your goal is not just limited to Graduating from prestigious Delhi university. It has to be bigger than that.Thanks for reading such a long answer. Appreciate my effort & Please share and up-vote if you find it valuable. Sharing will help more students like us. You may save a depression or even suicide.P.S - Talk about it to your parents, elder siblings. They are all supportive to you (Some cried over phone). Read more ordeals/opinions in the comment box. Rest you are mature enough to be like Phoenix 💪✍.Best Of Luck 🤞