JEE MAIN Definite Integration Previous Year Questions (PYQs) – Page 6 of 17
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The value of $\displaystyle \int_{-\pi/2}^{\pi/2} \frac{\sin^{2}x}{1+2^{x}},dx$ is :
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Solution
The integral
$\int_{0}^{\tfrac{\pi}{2}} \dfrac{1}{3 + 2 \sin x + \cos x} , dx$
is equal to :
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Solution
The function $I(x)=\int e^{\sin^{2}x},(\cos x\sin 2x-\sin x),dx$ with $I(0)=1$. Then $I!\left(\dfrac{\pi}{3}\right)$ is equal to:
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Solution
If $f(\alpha)=\int\limits_{1}^{\alpha} \frac{\log _{10} \mathrm{t}}{1+\mathrm{t}} \mathrm{dt}, \alpha>0$ then $f\left(\mathrm{e}^{3}\right)+f\left(\mathrm{e}^{-3}\right)$ is equal to :
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Solution
Let, for some function $y=f(x)$, $\displaystyle \int_{0}^{x} t,f(t),dt = x^{2}f(x)$ for $x>0$ and $f(2)=3$. Then $f(6)$ is equal to
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Solution
The value of the integral $\displaystyle \int_{0}^{1} \frac{\sqrt{x}\,dx}{(1+x)(1+3x)(3+x)}$ is:
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Solution
For $x\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)$, if
$y(x)=\displaystyle\int \frac{\csc x+\sin x}{\csc x\sec x+\tan x\sin^2 x}\,dx$,
and $\displaystyle\lim_{x\to \left(\frac{\pi}{2}\right)} y(x)=0$, then $y\!\left(\dfrac{\pi}{4}\right)$ is equal to:
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Solution
$\displaystyle \int_{0}^{\pi/4}\frac{\cos^{2}x,\sin^{2}x}{\big(\cos^{3}x+\sin^{3}x\big)^{2}},dx$ is equal to:
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Solution
If ${b_n} = \int_0^{{\pi \over 2}} {{{{{\cos }^2}nx} \over {\sin x}}dx,\,n \in N} $, then
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Solution
The integral $\int\limits_1^e {\left\{ {{{\left( {{x \over e}} \right)}^{2x}} - {{\left( {{e \over x}} \right)}^x}} \right\}} \,$ loge x dx is equal to :
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Solution
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