Definite Integration PYQs - Last 10 Years
JEE Advanced / Mathematics / Calculus / 21 recent questions
MathematicsCalculus2017-2026
Practice 21 JEE Advanced Mathematics questions from Definite Integration. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
21
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Mathematics / Calculus
2017-2026
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2022-2026
21
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2017-2026
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21PYQs
INTEGER57.1%
MCQM23.8%
MCQ19%
Difficulty Mix
#1 Medium11
#2 Hard8
#3 Easy2
8 in last 5 years21 in last 10 years
Last 10 Years Definite Integration Questions
Showing 21 of 21 filtered questions.
1Definite Integration
The value of the definite integral\(\int\limits_{0}^{2} \frac{1}{3^x + 3} dx\)is
MCQ+3 / -12026
2Definite Integration
If
\(\alpha=\int\limits_{\frac{1}{2}}^2 \frac{\tan ^{-1} x}{2 x^2-3 x+2} d x\)
then the value of $\sqrt{7} \tan \left(\frac{2 \alpha \sqrt{7}}{\pi}\right)$ is _________.
(Here, the inverse trigonometric function $\tan ^{-1} x$ assumes val...
\(\alpha=\int\limits_{\frac{1}{2}}^2 \frac{\tan ^{-1} x}{2 x^2-3 x+2} d x\)
then the value of $\sqrt{7} \tan \left(\frac{2 \alpha \sqrt{7}}{\pi}\right)$ is _________.
(Here, the inverse trigonometric function $\tan ^{-1} x$ assumes val...
INTEGER+4 / -02025
3Definite Integration
The value of $\frac{16}{\pi^3} \int\limits_0^{\frac{\pi}{2}} f(x) g(x) d x$ is ______.
INTEGER+3 / -02024
4Definite Integration
The value of $2 \int\limits_0^{\frac{\pi}{2}} f(x) g(x) d x-\int\limits_0^{\frac{\pi}{2}} g(x) d x$ is ____________.
INTEGER+3 / -02024
5Definite Integration
For $x \in \mathbb{R}$, let $\tan ^{-1}(x) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. Then the minimum value of the function $f: \mathbb{R} \rightarrow \mathbb{R}$ defined by $f(x)=\int\limits_0^{x \tan ^{-1} x} \frac{e^{(t-\cos t)}}{1...
INTEGER+4 / -02023
6Definite Integration
Let $f:(0,1) \rightarrow \mathbb{R}$ be the function defined as $f(x)=\sqrt{n}$ if $x \in\left[\frac{1}{n+1}, \frac{1}{n}\right)$ where $n \in \mathbb{N}$. Let $g:(0,1) \rightarrow \mathbb{R}$ be a function such that $\int\limits_{x^2}^x \s...
MCQ+3 / -12023
7Definite Integration
The greatest integer less than or equal to
\(\int_{1}^{2} \log _{2}\left(x^{3}+1\right) d x+\int_{1}^{\log _{2} 9}\left(2^{x}-1\right)^{\frac{1}{3}} d x\)
is ___________.
\(\int_{1}^{2} \log _{2}\left(x^{3}+1\right) d x+\int_{1}^{\log _{2} 9}\left(2^{x}-1\right)^{\frac{1}{3}} d x\)
is ___________.
INTEGER+3 / -12022
8Definite Integration
Consider the equation
\(\int_{1}^{e} \frac{\left(\log _{\mathrm{e}} x\right)^{1 / 2}}{x\left(a-\left(\log _{\mathrm{e}} x\right)^{3 / 2}\right)^{2}} d x=1, \quad a \in(-\infty, 0) \cup(1, \infty)\)
Which of the following statements is/ar...
\(\int_{1}^{e} \frac{\left(\log _{\mathrm{e}} x\right)^{1 / 2}}{x\left(a-\left(\log _{\mathrm{e}} x\right)^{3 / 2}\right)^{2}} d x=1, \quad a \in(-\infty, 0) \cup(1, \infty)\)
Which of the following statements is/ar...
MCQM+4 / -22022
9Definite Integration
For any real number x, let [ x ] denote the largest integer less than or equal to x. If \(I = \int\limits_0^{10} {\left[ {\sqrt {{{10x} \over {x + 1}}} } \right]dx}\), then the value of 9I is __________.
INTEGER+4 / -02021
10Definite Integration
Which of the following statements is TRUE?
MCQ+3 / -12021
11Definite Integration
Which of the following statements is TRUE?
MCQ+3 / -12021
12Definite Integration
Let \({g_i}:\left[ {{\pi \over 8},{{3\pi } \over 8}} \right] \to R,i = 1,2\), and \(f:\left[ {{\pi \over 8},{{3\pi } \over 8}} \right] \to R\) be functions such that \({g_1}(x) = 1,{g_2}(x) = |4x - \pi |\) and \(f(x) = {\sin ^2}x\), for a...
INTEGER+2 / -02021
13Definite Integration
Let \({g_i}:\left[ {{\pi \over 8},{{3\pi } \over 8}} \right] \to R,i = 1,2\), and \(f:\left[ {{\pi \over 8},{{3\pi } \over 8}} \right] \to R\) be functions such that \({g_1}(x) = 1,{g_2}(x) = |4x - \pi |\) and \(f(x) = {\sin ^2}x\), for a...
INTEGER+2 / -02021
14Definite Integration
Let \(f:\left[ { - {\pi \over 2},{\pi \over 2}} \right] \to R\) be a continuous function such that \(f(0) = 1\) and \(\int_0^{{\pi \over 3}} {f(t)dt = 0}\). Then which of the following statements is(are) TRUE?
MCQM+4 / -22021
15Definite Integration
Let b be a nonzero real number. Suppose f : R \(\to\) R is a differentiable function such that f(0) = 1. If the derivative f' of f satisfies the equation \(f'(x) = {{f(x)} \over {{b^2} + {x^2}}}\)for all x\(\in\)R, then which of the fol...
MCQM+4 / -22020
16Definite Integration
Let \(f:R \to R\) be a differentiable function such that its derivative f' is continuous and f(\(\pi\)) = \(-\)6.If \(F:[0,\pi ] \to R\) is defined by \(F(x) = \int_0^x {f(t)dt}\), and if \(\int_0^\pi {(f'(x)} + F(x))\cos x\,dx\) = 2the...
INTEGER+4 / -02020
17Definite Integration
Which of the following inequalities is/are TRUE?
MCQM+4 / -22020
18Definite Integration
The value of the integral \(\int\limits_0^{\pi /2} {{{3\sqrt {\cos \theta } } \over {{{(\sqrt {\cos \theta } + \sqrt {\sin \theta } )}^5}}}} d\theta\) equals ..............
INTEGER+3 / -02019
19Definite Integration
If \(I = {2 \over \pi }\int\limits_{ - \pi /4}^{\pi /4} {{{dx} \over {(1 + {e^{\sin x}})(2 - \cos 2x)}}}\), then 27I2 equals .................
INTEGER+3 / -02019
20Definite Integration
The value of the integral\(\int_0^{1/2} {{{1 + \sqrt 3 } \over {{{({{(x + 1)}^2}{{(1 - x)}^6})}^{1/4}}}}dx}\) is ........
INTEGER+3 / -02018
21Definite Integration
If \(I = \sum\nolimits_{k = 1}^{98} {\int_k^{k + 1} {{{k + 1} \over {x(x + 1)}}} dx}\), then
MCQM+4 / -22017