Application of Integration PYQs - Last 10 Years
JEE Advanced / Mathematics / Calculus / 16 recent questions
MathematicsCalculus2017-2026
Practice 16 JEE Advanced Mathematics questions from Application of Integration. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
16
PYQs on Page
Mathematics / Calculus
2017-2026
Year Range
Based on indexed question metadata
7
Last 5 Years
2022-2026
16
Last 10 Years
2017-2026
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20214 max PYQs/year2026
Question Types
16PYQs
INTEGER50%
MCQ31.3%
MCQM18.8%
Difficulty Mix
#1 Medium8
#2 Hard7
#3 Easy1
7 in last 5 years16 in last 10 years
Last 10 Years Application of Integration Questions
Showing 16 of 16 filtered questions.
1Application Of Integration
Consider the ellipses given by
\(x^2+4 y^2=1 \quad \text { and } \quad 4 x^2+y^2=1 .\)
If $\alpha$ is the area of the common region that lies inside both the given ellipses, then the value of $\cot \alpha$ is $\_\_\_\_$ .
\(x^2+4 y^2=1 \quad \text { and } \quad 4 x^2+y^2=1 .\)
If $\alpha$ is the area of the common region that lies inside both the given ellipses, then the value of $\cot \alpha$ is $\_\_\_\_$ .
INTEGER+2 / -02026
2Application Of Integration
Consider the curve $C_1$ given by
\(y=e^{-x} \quad \text { for } x \in[0,10 \pi],\)
and the curve $C_2$ given by
\(y=e^{-x}(\sin x+\cos x) \quad \text { for } x \in[0,10 \pi] .\)
Let $n$ be the total number of points of intersection of ...
\(y=e^{-x} \quad \text { for } x \in[0,10 \pi],\)
and the curve $C_2$ given by
\(y=e^{-x}(\sin x+\cos x) \quad \text { for } x \in[0,10 \pi] .\)
Let $n$ be the total number of points of intersection of ...
INTEGER+2 / -02026
3Application Of Integration
Let ℝ denote the set of all real numbers. Then the area of the region
$ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x}, 5x - 4y - 1 > 0, 4x + 4y - 17 < 0 \right\} $
is
$ \left\{ (x, y) \in \mathbb{R} \times \mathbb{R} : x > 0, y > \frac{1}{x}, 5x - 4y - 1 > 0, 4x + 4y - 17 < 0 \right\} $
is
MCQ+3 / -12025
4Application Of Integration
Let the function $f:[1, \infty) \rightarrow \mathbb{R}$ be defined by
$$ f(t)=\left\{\begin{array}{cc} (-1)^{n+1} 2, & \text { if } t=2 n-1, n \in \mathbb{N}, \\ \frac{(2 n+1-t)}{2} f(2 n-1)+\frac{(t-(2 n-1))}{2} f(2 n+1), & \text { if } 2...
$$ f(t)=\left\{\begin{array}{cc} (-1)^{n+1} 2, & \text { if } t=2 n-1, n \in \mathbb{N}, \\ \frac{(2 n+1-t)}{2} f(2 n-1)+\frac{(t-(2 n-1))}{2} f(2 n+1), & \text { if } 2...
INTEGER+4 / -02024
5Application Of Integration
Let $S=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}: x \geq 0, y \geq 0, y^2 \leq 4 x, y^2 \leq 12-2 x\right.$ and $\left.3 y+\sqrt{8} x \leq 5 \sqrt{8}\right\}$. If the area of the region $S$ is $\alpha \sqrt{2}$, then $\alpha$ is equal ...
MCQ+3 / -12024
6Application Of Integration
Let $n \geq 2$ be a natural number and $f:[0,1] \rightarrow \mathbb{R}$ be the function defined by
$$
f(x)= \begin{cases}n(1-2 n x) & \text { if } 0 \leq x \leq \frac{1}{2 n} \\\\ 2 n(2 n x-1) & \text { if } \frac{1}{2 n} \leq x \leq \frac{...
$$
f(x)= \begin{cases}n(1-2 n x) & \text { if } 0 \leq x \leq \frac{1}{2 n} \\\\ 2 n(2 n x-1) & \text { if } \frac{1}{2 n} \leq x \leq \frac{...
INTEGER+4 / -02023
7Application Of Integration
Consider the functions $f, g: \mathbb{R} \rightarrow \mathbb{R}$ defined by
$$
f(x)=x^{2}+\frac{5}{12} \quad \text { and } \quad g(x)= \begin{cases}2\left(1-\frac{4|x|}{3}\right), & |x| \leq \frac{3}{4} \\ 0, & |x|>\frac{3}{4}\end{cases}
$...
$$
f(x)=x^{2}+\frac{5}{12} \quad \text { and } \quad g(x)= \begin{cases}2\left(1-\frac{4|x|}{3}\right), & |x| \leq \frac{3}{4} \\ 0, & |x|>\frac{3}{4}\end{cases}
$...
INTEGER+3 / -12022
8Application Of Integration
Let f1 : (0, \(\infty\)) \(\to\) R and f2 : (0, \(\infty\)) \(\to\) R be defined by \({f_1}(x) = \int\limits_0^x {\prod\limits_{j = 1}^{21} {{{(t - j)}^j}dt} }\), x > 0 and \({f_2}(x) = 98{(x - 1)^{50}} - 600{(x - 1)^{49}} + 2450,x > 0\), ...
INTEGER+2 / -02021
9Application Of Integration
Let f1 : (0, \(\infty\)) \(\to\) R and f2 : (0, \(\infty\)) \(\to\) R be defined by \({f_1}(x) = \int\limits_0^x {\prod\limits_{j = 1}^{21} {{{(t - j)}^j}dt} }\), x > 0 and \({f_2}(x) = 98{(x - 1)^{50}} - 600{(x - 1)^{49}} + 2450,x > 0\), ...
INTEGER+2 / -02021
10Application Of Integration
For any real numbers \(\alpha\) and \(\beta\), let \({y_{\alpha ,\beta }}(x)\), x\(\in\)R, be the solution of the differential equation \({{dy} \over {dx}} + \alpha y = x{e^{\beta x}},y(1) = 1\). Let $$S = \{ {y_{\alpha ,\beta }}(x):\alpha ...
MCQM+4 / -22021
11Application Of Integration
The area of the region \(\left\{ {\matrix{
{(x,y):0 \le x \le {9 \over 4},} & {0 \le y \le 1,} & {x \ge 3y,} & {x + y \ge 2} \cr
} } \right\}\) is
MCQ+3 / -12021
12Application Of Integration
Let the functions f : R \(\to\) R and g : R \(\to\) R be defined byf(x) = ex \(-\) 1 \(-\) e\(-\)|x \(-\) 1|and g(x) = \({1 \over 2}\)(ex \(-\) 1 + e1 \(-\) x).The the area of the region in the first quadrant bounded by the curves y = f...
MCQ+3 / -12020
13Application Of Integration
The area of the region{(x, y) : xy \(\le\) 8, 1 \(\le\) y \(\le\) x2} is
MCQ+3 / -12019
14Application Of Integration
Let f : [0, \(\infty\)) \(\to\) R be a continuous function such that\(f(x) = 1 - 2x + \int_0^x {{e^{x - t}}f(t)dt}\) for all x \(\in\) [0, \(\infty\)). Then, which of the following statement(s) is (are) TRUE?
MCQM+4 / -12018
15Application Of Integration
A farmer F1 has a land in the shape of a triangle with vertices at P(0, 0), Q(1, 1) and R(2, 0). From this land, a neighbouring farmer F2 takes away the region which lies between the sides PQ and a curve of the form y = xn (n > 1). If the a...
INTEGER+3 / -02018
16Application Of Integration
If the line x = \(\alpha\) divides the area of region R = {(x, y) \(\in\)R2 : x3 \(\le\) y \(\le\) x, 0 \(\le\) x \(\le\) 1} into two equal parts, then
MCQM+4 / -22017