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We want to evaluate the integral[math]I = \displaystyle \int_0^{\infty} e^{-x^3} \sin(x^3) [/math][math][/math][math]\, dx. \tag*{}[/math]First, we let [math]t = x^3[/math]:[math]I = \displaystyle \frac{1}{3} \int_0^{\infty} e^{-t} t^{-2/3} \sin{t} [/math][math][/math][math]\, dt. \tag*{}[/math]To facilitate evaluating this latter integral, we use Euler’s Identity, noting that [math]\sin{t}[/math] is the imaginary part of [math]e^{it}[/math]:[math]\begin{align*} I &= \displaystyle \frac{1}{3} \int_0^{\infty} e^{-t} t^{-2/3} \sin{t} [/math][math][/math][math]\, dt\\ &= \displaystyle \frac{1}{3} \cdot \text{Im [/math][math][/math][math]} \int_0^{\infty} e^{-(1-i)t} t^{-2/3} [/math][math][/math][math]\, dt\\ &= \displaystyle \frac{1}{3} \cdot \text{Im [/math][math][/math][math]} (1-i)^{-1/3} \int_0^{\infty} e^{-y} y^{-2/3} [/math][math][/math][math]\, dy, \text{ via [/math][math][/math][math]} y = (1-i)t\\ [/math][math][/math][math] &= \displaystyle \frac{1}{3} \cdot \text{Im [/math][math][/math][math]} (\sqrt{2} e^{-\pi i/4})^{-1/3} \cdot \Gamma\Big(\frac{1}{3}\Big) [/math][math][/math][math]\\ &= \displaystyle \frac{1}{3 \cdot 2^{1/6}} \Gamma\Big(\frac{1}{3}\Big) [/math][math][/math][math] \sin\Big(\frac{\pi}{12}\Big)\\ &= \displaystyle \frac{1}{3\cdot 2^{1/6}} \Gamma\Big(\frac{1}{3}\Big) \sin\Big(\frac{\pi}{3} - \frac{\pi}{4}\Big)\\ &= \displaystyle \frac{1}{3\cdot 2^{1/6}} \Gamma\Big(\frac{1}{3}\Big) \Big(\sin{\frac{\pi}{3}} \cos{\frac{\pi}{4}} - \cos{\frac{\pi}{3}} \sin{\frac{\pi}{4}}\Big)\\ &= \displaystyle \frac{\sqrt{3} - 1}{3 \cdot 2^{5/3}} \Gamma\Big(\frac{1}{3}\Big). \end{align*} \tag*{}[/math]Hence, we conclude that[math]\displaystyle \int_0^{\infty} e^{-x^3} \sin(x^3) [/math][math][/math][math]\, dx = \frac{\sqrt{3} - 1}{3 \cdot 2^{5/3}} \Gamma\Big(\frac{1}{3}\Big) \approx 0.205905. \tag*{}[/math](Exact value double checked on Wolfram Alpha.)

Applicants are evaluated based on GMAT/CAT/XAT/CMAT scores, past academic performance, essays, work experience and performance in the personal interview. The selection process builds in a criterion that facilitates evaluating each applicant on Academic Abilities, Standardized Test Scores, Rank Holders, Integrity & Ethical Values and Diversity of Background.At Great Lakes, we do not have fixed cut-offs, we try to evaluate candidates in a holistic manner. We consider the complete profile, so while the test scores are important, we emphasize more on selecting well-rounded candidates with a strong overall track record.

I am familiar with three theories of mediation. Facilitative, evaluative and transformative. Each can be used with respect for any type of conflict, but transformative is often recommended in situations where the parties have an ongoing relationship and I see evaluative used in a fashion similar to a settlement conference in litigation. To learn more about transformative mediation, you may enjoy Bush & Folger's "The Promise of Mediation."