Definite Integration PYQs - Last 5 Years
JEE Advanced / Mathematics / Calculus / 8 recent questions
MathematicsCalculus2022-2026
Practice 8 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.
8
PYQs on Page
Mathematics / Calculus
2022-2026
Year Range
Based on indexed question metadata
8
Last 5 Years
2022-2026
8
Last 10 Years
2017-2026
Recent Year Trend
2022
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20222 max PYQs/year2026
Question Types
8PYQs
INTEGER62.5%
MCQ25%
MCQM12.5%
Difficulty Mix
#1 Hard5
#2 Medium2
#3 Easy1
8 in last 5 years8 in last 10 years
Last 5 Years Definite Integration Questions
Showing 8 of 8 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