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Question Number 44232 by LYCON TRIX last updated on 24/Sep/18

$${\int }_0^{\pi }{\mathrm{e}}^{{\sin }^2\mathrm{x}}{\mathrm{Cos}}^3\mathrm{xdx}$$

Answered by tanmay.chaudhury50@gmail.com last updated on 24/Sep/18

$$f\left(x\right)=e^{{sin}^{2}x}{cos}^{3}x$$$$f(\mathrm{\Pi }-x)=e^{{\left\{sin(\mathrm{\Pi }-x)\right\}}^2}{\left\{cos(\mathrm{\Pi }-x)\right\}}^3$$$$=e^{{sin}^{2}x}\times {(-cosx)}^3$$$$=-f\left(x\right)$$$$so{\int }_0^{\mathrm{\Pi }}{e}^{{sin}^{2}x}{cos}^{3}xdx=0$$

Commented by tanmay.chaudhury50@gmail.com last updated on 24/Sep/18

Commented by Hitarth Rana last updated on 24/Sep/18

$$Perfect...★★★★★$$

Commented by LYCON TRIX last updated on 24/Sep/18

$$\mathrm{Thanks}\mathrm{a}\mathrm{lot}\mathrm{gentlemen}$$

Commented by tanmay.chaudhury50@gmail.com last updated on 24/Sep/18

$$thankyou...$$

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