definite-integral

Related Questions

• $\int_{0}^{\pi /2}{{{e}^{x}}\sin x\,dx=}$

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• $\int_{\,0}^{\,1}{\frac{d}{dx}\left[ {{\sin }^{-1}}\left( \frac{2x}{1+{{x}^{2}}} \right) \right]\,dx}$ is equal to

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• Let $f(x)$ be a non-negative continous function such that the area bounded by the curve $y=f(x)$, x-axis and the ordinates $x=\frac{\pi }{4}$, $x=\beta >\frac{\pi }{4}$ is $\left( \beta \sin \beta +\frac{\pi }{4}\cos \beta +\sqrt{2}\beta \right)$. Then $f\ \left( \frac{\pi }{2} \right)$ is

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• Let ${{I}_{1}}=\int_{a}^{\pi -a}{xf(\sin x)dx,\,{{I}_{2}}=\int_{a}^{\pi -a}{\,\,f(\sin x)dx}}$, then ${{I}_{2}}$ is equal to

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• $\int_{-1}^{1}{\log \frac{2-x}{2+x}\,dx}=$

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