Definite Integration PYQs - Last 5 Years
IAT (IISER) / Mathematics / Calculus / 8 recent questions
MathematicsCalculus2022-2026
Practice 8 IAT (IISER) Mathematics questions from Definite Integration. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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Mathematics / Calculus
2022-2026
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2017-2026
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8 in last 5 years8 in last 10 years
Last 5 Years Definite Integration Questions
Showing 8 of 8 filtered questions.
1Definite Integration
What is the value of $\displaystyle\int_{-1}^{2} \min\{1 - x, 1 - x^3\}\, dx$?
MCQ+4 / -12026
2Definite Integration
What is the value of $\int_0^\pi x|\cos x| \sin x d x$ ?
MCQ+4 / -12025
3Definite Integration
Let $I=\int_{e^{-\pi / 2}}^{e^{\pi / 2}}\left(\sin ^2(\log (x))+\sin \left(\log \left(x^2\right)\right)\right) d x$. What is the value of $I$ ?
MCQ+4 / -12024
4Definite Integration
Let $f: \mathbf{R} \rightarrow(0, \infty)$ be a continuous decreasing function. Suppose $f(0), \dot{f}(1), \ldots, f(10)$ are in a geometric progression with common ratio $\frac{1}{5}$. In which of the following intervals does the value of ...
MCQ+4 / -12023
5Definite Integration
Let $f:(-1,2) \rightarrow \mathbf{R}$ be a differentiable function such that $f^{\prime}(x)=\frac{2}{x^2-5}$ and $f(0)=0$. Then in which of the following intervals does $f(1)$ lie?
MCQ+4 / -12023
6Definite Integration
The value of the integral
\(\int_1^{100} \frac{[x]}{x} d x\)
where $[x]$ is the greatest integer less than or equal to $x$ for any real number $x$, is
\(\int_1^{100} \frac{[x]}{x} d x\)
where $[x]$ is the greatest integer less than or equal to $x$ for any real number $x$, is
MCQ+4 / -12022
7Definite Integration
For a natural number $n$, let $C_n$ be the curve in the $X Y$-plane given by $y=x^n$, where $0 \leq$ $x \leq 1$. Let $A_n$ denote the area of the region bounded between $C_n$ and $C_n+1$. Then the largest value of $A_n$ is
MCQ+4 / -12022
8Definite Integration
Let $f$ be a continuous function on $[0,1]$ and $F$ be its antiderivative. If $F(0)=1$ and $\int_0^1 f(x) d x=1$, then $F(1)$ is
MCQ+4 / -12022