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DEFINITE INTEGRATION

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE MAIN 2023
The value of $\frac{e^{-\pi / 4}+\int_0^{\pi / 4} e^{-x} \tan ^{50} x d x}{\int_0^{\pi / 4} e^{-x}\left(\tan ^{49} x+\tan ^{51} x\right) d x}$
JEE Main Mathematics Hard
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Q JEE MAIN 2025
Let $f(x)$ be a positive function and $I_1=\int_{-\frac{1}{2}}^1 2 x f(2 x(1-2 x)) d x$ and $I_2=\int_{-1}^2 f(x(1-x)) d x$. Then the value of $\frac{I_2}{I_1}$...
JEE Main Mathematics Medium
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Q JEE MAIN 2023
Let $f(x)$ be a function satisfying $f(x)+f(\pi-x)=\pi^2, \forall x \in R$. Then $\int^\pi f(x) \sin x d x$ is equal to
JEE Main Mathematics Easy
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Q JEE MAIN 2025
The integral $\int_{-1}^{\frac{3}{2}}\left(\left|\pi^2 x \sin (\pi x)\right|\right) d x$ is equal to :
JEE Main Mathematics Hard
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Q JEE MAIN 2023
Let $f$ be a continuous function satisfying $\int_0^{t^2}\left(f(x)+x^2\right) d x=\frac{4}{3} t^3, \forall t>0$. Then $f\left(\frac{\pi^2}{4}\right)$ is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN 2025
$4 \int_0^1\left(\frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}}\right) d x-3 \log _e(\sqrt{3})$ is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN 2025
Let $\quad f(x)+2 f\left(\frac{1}{x}\right)=x^2+5 \quad$ and $\quad 2 g(x)-3 g\left(\frac{1}{2}\right)=x, x>0$. If $\quad \alpha=\int_1^2 f(x) \mathrm{d} x, \quad$ and $\beta=\int_1^2 \mathrm{~g}(x) \mathrm{d} x$, then the...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Let $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function. If $10 \int_1^x f(t) d t=5 x f(x)-x^5-9$ for all $x \geqslant 1$, then the value...
JEE Main Mathematics Hard
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Q JEE MAIN 2025
Let $(a, b)$ be the point of intersection of the curve $x^2=2 y$ and the straight line $y-2 x-6=0$ in the second quadrant. Then the...
JEE Main Mathematics Medium
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Q JEE MAIN 2025
The integral $\int_0^\pi \frac{8 x d x}{4 \cos ^2 x+\sin ^2 x}$ is equal to
JEE Main Mathematics Easy
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