My Cart
Your Cart 0

    Your cart is empty.

  • Total (Amount) ₹0.00
Previous year question hub

Application Of Integration - Calculus - Mathematics Previous Year Questions

Practice Application Of Integration - Calculus - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

19Papers
18Years
22Questions
1Topics

Application Of Integration question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Application Of Integration. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Hard 12 54.5%
Medium 7 31.8%
Not classified 3 13.6%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Subjective 16 72.7%
Multiple Choices 3 13.6%
Numerical Answer Type (NAT) 3 13.6%

Subject weightage

Top subjects by unique question coverage.

Mathematics
22 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
22 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Application Of Integration
22 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

JEE Advanced 2026 Paper 2 Online
2 Qs
JEE ADVANCED 2022 PAPER 2 ONLINE
1 Qs
IIT JEE 2006
1 Qs
IIT JEE 2005
2 Qs
IIT JEE 2005 MAINS
2 Qs
IIT JEE 2002
1 Qs
IIT JEE 2001
1 Qs
IIT JEE 1999
1 Qs
IIT JEE 1997
1 Qs
IIT JEE 1995
1 Qs
IIT JEE 1992
1 Qs
IIT JEE 1991
1 Qs
IIT JEE 1990
1 Qs
IIT JEE 1988
1 Qs
IIT JEE 1987
1 Qs
IIT JEE 1985
1 Qs
IIT JEE 1984
1 Qs
IIT JEE 1983
1 Qs
IIT JEE 1981
1 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
JEE Advanced 2026 Paper 2 Online20262View paper
JEE ADVANCED 2022 PAPER 2 ONLINE20221View paper
IIT JEE 200620061View paper
IIT JEE 200520052View paper
IIT JEE 2005 MAINS20052View paper
IIT JEE 200220021View paper
IIT JEE 200120011View paper
IIT JEE 199919991View paper
IIT JEE 199719971View paper
IIT JEE 199519951View paper
IIT JEE 199219921View paper
IIT JEE 199119911View paper
IIT JEE 199019901View paper
IIT JEE 198819881View paper
IIT JEE 198719871View paper
IIT JEE 198519851View paper
IIT JEE 198419841View paper
IIT JEE 198319831View paper
IIT JEE 198119811View paper

All Application Of Integration previous year questions

Practice every matching question in batches of 20, with every available option.

1
1981 · Mathematics · Calculus · Application Of Integration
IIT JEE 1981
Find the area bounded by the curve \({x^2} = 4y\) and the straight
Write your response
Open complete paper
2
1983 · Mathematics · Calculus · Application Of Integration
IIT JEE 1983
Find the area bounded by the \(x\)-axis, part of the curve \(y = \left( {1 + {8 \over {{x^2}}}} \right)\) and
the ordinates at \(x=2\) and \(x=4\). If the ordinate at \(x=a\) divides the area into two equal parts, find \(a\).
Write your response
Open complete paper
3
1984 · Mathematics · Calculus · Application Of Integration
IIT JEE 1984
Find the area of the region bounded by the \(x\)-axis and the curves defined by \(y = \tan x, - {\pi \over 3} \le x \le {\pi \over 3};\,\,y = \cot x,{\pi \over 6} \le x \le {{3\pi } \over 2}\)
Write your response
Open complete paper
4
1985 · Mathematics · Calculus · Application Of Integration
IIT JEE 1985
Sketch the region bounded by the curves \(y = \sqrt {5 - {x^2}}\) and \(y = \left| {x - 1} \right|\) and find its area.
Write your response
Open complete paper
5
1987 · Mathematics · Calculus · Application Of Integration
IIT JEE 1987
Find the area bounded by the curves, \({x^2} + {y^2} = 25,\,4y = \left| {4 - {x^2}} \right|\) and \(x=0\) above the \(x\)-axis.
Write your response
Open complete paper
6
1988 · Mathematics · Calculus · Application Of Integration
IIT JEE 1988
Find the area of the region bounded by the curve \(C:y=\)
\(\tan x,\) tangent drawn to \(C\) at \(x = {\pi \over 4}\) and the \(x\)-axis.
Write your response
Open complete paper
7
1990 · Mathematics · Calculus · Application Of Integration
IIT JEE 1990
Compute the area of the region bounded by the curves \(\,y = ex\,\ln x\) and \(y = {{\ln x} \over {ex}}\) where \(ln\) \(e=1.\)
Write your response
Open complete paper
8
1991 · Mathematics · Calculus · Application Of Integration
IIT JEE 1991
Sketch the curves and identify the region bounded by
\(x = {1 \over 2},x = 2,y = \ln \,x\) and \(y = {2^x}.\) Find the area of this region.
Write your response
Open complete paper
9
1992 · Mathematics · Calculus · Application Of Integration
IIT JEE 1992
Sketch the region bounded by the curves \(y = {x^2}\) and
\(y = {2 \over {1 + {x^2}}}.\) Find the area.
Write your response
Open complete paper
10
1995 · Mathematics · Calculus · Application Of Integration
IIT JEE 1995
Consider a square with vertices at \((1,1), (-1,1), (-1,-1)\) and \((1, -1)\). Let \(S\) be the region consisting of all points inside the square which are nearer to the origin than to any edge. Sketch the region \(S\) and find its area.
Write your response
Open complete paper
11
1997 · Mathematics · Calculus · Application Of Integration
IIT JEE 1997
Let \(f(x)= Maximum\) \(\,\left\{ {{x^2},{{\left( {1 - x} \right)}^2},2x\left( {1 - x} \right)} \right\},\) where \(0 \le x \le 1.\)
Determine the area of the region bounded by the curves
\(y = f\left( x \right),\) \(x\)-axes, \(x=0\) and \(x=1.\)
Write your response
Open complete paper
12
1999 · Mathematics · Calculus · Application Of Integration
IIT JEE 1999
Let \(f(x)\) be a continuous function given by \(f\left( x \right) = \left\{ {\matrix{ \[{2x,} & {\left| x \right| \le 1} \cr\] \[{{x^2} + ax + b,} & {\left| x \right| > 1} \cr\] } } \right\}\)

Find the area of the region in the third quadrant bounded by the curves \(x = - 2{y^2}\) and \(y=f(x)\) lying on the left of the line \(8x+1=0.\)

Write your response
Open complete paper
13
2001 · Mathematics · Calculus · Application Of Integration
IIT JEE 2001
Let \(b \ne 0\) and for \(j=0, 1, 2, ..., n,\) let \({S_j}\) be the area of
the region bounded by the \(y\)-axis and the curve \(x{e^{ay}} = \sin\) by,
\({{jr} \over b} \le y \le {{\left( {j + 1} \right)\pi } \over b}.\) Show that \({S_0},{S_1},{S_2},\,....,\,{S_n}\) are in
geometric progression. Also, find their sum for \(a=-1\) and \(b = \pi .\)
Write your response
Open complete paper
14
2002 · Mathematics · Calculus · Application Of Integration
IIT JEE 2002
Find the area of the region bounded by the curves \(y = {x^2},y = \left| {2 - {x^2}} \right|\) and \(y=2,\) which lies to the right of the line \(x=1.\)
Write your response
Open complete paper
15
2005 · Mathematics · Calculus · Application Of Integration
IIT JEE 2005
Find the area bounded by the curves \({x^2} = y,{x^2} = - y\) and \({y^2} = 4x - 3.\)
Write your response
Open complete paper
16
2005 · Mathematics · Calculus · Application Of Integration
IIT JEE 2005
If \(\left[ {\matrix{ {4{a^2}} & {4a} & 1 \cr {4{b^2}} & {4b} & 1 \cr {4{c^2}} & {4c} & 1 \cr } } \right]\left[ {\matrix{ \[{f\left( { - 1} \right)} \cr\] \[{f\left( 1 \right)} \cr\] \[{f\left( 2 \right)} \cr\] } } \right] = \left[ {\matrix{ {3{a^2} + 3a} \cr {3{b^2} + 3b} \cr {3{c^2} + 3c} \cr } } \right],\,\,f\left( x \right)\) is a quadratic
function and its maximum value occurs at a point \(V\). \(A\) is a point of intersection of \(y=f(x)\) with \(x\)-axis and point \(B\) is such that chord \(AB\) subtends a right angle at \(V\). Find the area enclosed by \(f(x)\) and chord \(AB\).
Write your response
Open complete paper
17
2005 · Mathematics · Calculus · Application Of Integration
IIT JEE 2005 MAINS

If length of tangent at any point on the curve \(y = f(x)\) intercepted between the point and the X-axis is of length 1. Find the equation of the curve.

A
\(\sqrt{1-y^{2}}-\frac{1}{2} \log \left|\frac{1+\sqrt{1-y^{2}}}{1-\sqrt{1-y^{2}}}\right|= \pm x+c\)
B
\(\sqrt{1-y^{2}}- \log \left|\frac{1+\sqrt{1-y^{2}}}{1-\sqrt{1-y^{2}}}\right|= \pm x+c\)
C
\(\sqrt{1-y^{2}}+\frac{1}{2} \log \left|\frac{1+\sqrt{1-y^{2}}}{1-\sqrt{1-y^{2}}}\right|= \pm x+c\)
D
\(\sqrt{1-y^{2}}-\frac{1}{2} \log \left|\frac{1+\sqrt{1-y^{2}}}{1-\sqrt{1-y^{2}}}\right|= \pm 5x+c\)
Open complete paper
18
2005 · Mathematics · Calculus · Application Of Integration
IIT JEE 2005 MAINS

If \(\left[\begin{array}{lll}4 a^{2} & 4 a & 1 \\ 4 b^{2} & 4 b & 1 \\ 4 c^{2} & 4 c & 1\end{array}\right]\left[\begin{array}{c}f(-1) \\ f(1) \\ f(2)\end{array}\right]=\left[\begin{array}{c}3 a^{2}+3 a \\ 3 b^{2}+3 b \\ 3 c^{2}+3 c\end{array}\right], \quad f(x)\)

is a quadratic function and its maximum value occurs at a point \(\mathrm{V}\). If A is a point of intersection of \(y=f(x)\) with \(x\)-axis and point B is such that chord AB subtends a right angle at point \(\mathrm{V}\). Find the area enclosed by \(f(x)\) and chord AB.

A
\({{125} \over 3}\)
B
\({{125} \over 7}\)
C
\({{25} \over 3}\)
D
\({{23} \over 6}\)
Open complete paper
19
2006 · Mathematics · Calculus · Application Of Integration
IIT JEE 2006

$$\text { Match the following : }$$

(i) $$
\[\int_0^{\pi / 2}(\sin x)^{\cos x}\left(\cos x \cot x-\log \left(\sin ^x\right)^{\sin } x\right) \mathrm{d} x\]
$$		 (A) 1
(ii) $$
\[\text { Area bounded by }-4 y^2=x \text { and } x-1=-5 y^2\]
$$		 (B) 0
(iii) Cosine of the angle of intersection of $y=3^{x-1} \log x$ and $y=x^{x-1}$ is (C) 6 In 2
(iv) $$
\[\frac{d y}{d x}=\frac{2}{(x+y)} ; y\left(-\frac{2}{3}\right)=0 \text {, then value of constant }(\mathrm{k})=\]
$$		 (D) 4/3
A

\(\begin{aligned} & \text { (i)-(A); (ii)-(D); (iii)-(B); }\text { (iv)-(D) } \end{aligned}\)

B

\(\begin{aligned} & \text { (i)-(A); (ii)-(C); (iii)-(B); }\text { (iv)-(D) } \end{aligned}\)

C

\(\begin{aligned} & \text { (i)-(A); (ii)-(D); (iii)-(A); }\text { (iv)-(D) } \end{aligned}\)

D

\(\begin{aligned} & \text { (i)-(A); (ii)-(B); (iii)-(C); }\text { (iv)-(D) } \end{aligned}\)

Open complete paper
20
2022 · Mathematics · Calculus · Application Of Integration
JEE ADVANCED 2022 PAPER 2 ONLINE
Consider the functions $f, g: \mathbb{R} \rightarrow \mathbb{R}$ defined by

$$f(x)=x^{2}+\frac{5}{12} \quad \text { and } \quad g(x)= \begin{cases}2\left(1-\frac{4|x|}{3}\right), & |x| \leq \frac{3}{4} \\ 0, & |x|>\frac{3}{4}\end{cases}$$

If $\alpha$ is the area of the region

$$\left\{(x, y) \in \mathbb{R} \times \mathbb{R}:|x| \leq \frac{3}{4}, 0 \leq y \leq \min \{f(x), g(x)\}\right\},$$

then the value of $9 \alpha$ is
Enter a numerical response
Open complete paper

Showing 20 of 22 questions