definite-integral

Related Questions

• 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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• $\int_{0}^{2}{\frac{{{x}^{3}}\,dx}{{{({{x}^{2}}+1)}^{\frac{3}{2}}}}}=$

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• If $\varphi (x)=\int_{1/x}^{\sqrt{x}}{\sin ({{t}^{2}})\,dt,}$ then ${\varphi }'(1)=$

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• The area bounded by the curve $y=f(x)$, x-axis and ordinates x = 1 and $x=b$is $\frac{5}{24}\pi $, then $f(x)$ is

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• If a curve $y=a\sqrt{x}+bx$ passes through the point (1, 2) and the area bounded by the curve, line $x=4$ and x-axis is 8 sq. unit, then

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