definite-integral

Related Questions

• If for non-zero $x,$ $af(x)+bf\left( \frac{1}{x} \right)=\frac{1}{x}-5,$ where $a\ne b,$ then $\int_{1}^{2}{f(x)\,dx=}$

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• The value of the definite integral $\int_{0}^{1}{\frac{dx}{{{x}^{2}}+2x\cos \alpha +1}}$ for $0<\alpha <\pi $ is equal to

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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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• $\int_{\ -\pi }^{\pi }{\frac{{{\sin }^{4}}x}{{{\sin }^{4}}x+{{\cos }^{4}}x}\ dx}=$

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• $\int_{0}^{2\pi }{\frac{\sin 2\theta }{a-b\,\cos \theta }\,d\theta =}$

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