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Question Number 14395 by tawa tawa last updated on 31/May/17

$$\mathrm{Evaluate}{\int }_0^{\frac{\pi }{2}}\sin \left(2\mathrm{x}\right){\mathrm{e}}^{{\cos }^2\left(\mathrm{x}\right)}\mathrm{dx}$$

Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 31/May/17

$$u={cos}^{2}x\Rightarrow du=-2sinx.cosxdx=-sin2xdx$$$$I=\int -e^{u}du=-e^u+C=-e^{{cos}^{2}x}+C.$$$$I=F\left(\frac{\pi }{2}\right)-F\left(0\right)=-e^0+e^1=e-1.◼$$

Commented by tawa tawa last updated on 31/May/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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