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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.

47Papers
39Years
65Questions
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.

Medium 30 46.2%
Hard 26 40%
Not classified 7 10.8%
Easy 2 3.1%

Question type distribution

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

MCQ 27 41.5%
Subjective 20 30.8%
Numerical Answer Type (NAT) 10 15.4%
MSQ 8 12.3%

Subject weightage

Top subjects by unique question coverage.

Mathematics
65 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
65 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Application Of Integration
65 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 2025 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2024 PAPER 2 ONLINE
2 Qs
JEE ADVANCED 2023 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2022 PAPER 2 ONLINE
1 Qs
JEE ADVANCED 2021 PAPER 2 ONLINE
3 Qs
JEE ADVANCED 2021 PAPER 1 ONLINE
1 Qs
JEE ADVANCED 2020 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2019 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2018 PAPER 1 OFFLINE
2 Qs
JEE ADVANCED 2017 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2016 PAPER 2 OFFLINE
1 Qs
JEE ADVANCED 2015 PAPER 2 OFFLINE
2 Qs
JEE ADVANCED 2015 PAPER 1 OFFLINE
1 Qs
JEE ADVANCED 2013 PAPER 1 OFFLINE
1 Qs
IIT JEE 2012 PAPER 1 OFFLINE
1 Qs
IIT JEE 2011 PAPER 1 OFFLINE
1 Qs
IIT JEE 2011 PAPER 2 OFFLINE
1 Qs
IIT JEE 2010 PAPER 1 OFFLINE
1 Qs
IIT JEE 2010 PAPER 2 OFFLINE
1 Qs
IIT JEE 2009 PAPER 1 OFFLINE
2 Qs
IIT JEE 2008 PAPER 1 OFFLINE
1 Qs
IIT JEE 2008 PAPER 2 OFFLINE
1 Qs
IIT JEE 2006
4 Qs
IIT JEE 2005 MAINS
3 Qs
IIT JEE 2005
2 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2004 SCREENING
1 Qs
IIT JEE 2003 SCREENING
1 Qs
IIT JEE 2002 SCREENING
2 Qs
IIT JEE 2002
1 Qs
IIT JEE 2001
1 Qs
IIT JEE 1999
2 Qs
IIT JEE 1997
2 Qs
IIT JEE 1996
1 Qs
IIT JEE 1995
1 Qs
IIT JEE 1994
1 Qs
IIT JEE 1992
1 Qs
IIT JEE 1991
2 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 1982
2 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 2025 PAPER 2 ONLINE20251View paper
JEE ADVANCED 2024 PAPER 2 ONLINE20242View paper
JEE ADVANCED 2023 PAPER 1 ONLINE20231View paper
JEE ADVANCED 2022 PAPER 2 ONLINE20221View paper
JEE ADVANCED 2021 PAPER 1 ONLINE20211View paper
JEE ADVANCED 2021 PAPER 2 ONLINE20213View paper
JEE ADVANCED 2020 PAPER 1 OFFLINE20201View paper
JEE ADVANCED 2019 PAPER 1 OFFLINE20191View paper
JEE ADVANCED 2018 PAPER 1 OFFLINE20182View paper
JEE ADVANCED 2017 PAPER 2 OFFLINE20171View paper
JEE ADVANCED 2016 PAPER 2 OFFLINE20161View paper
JEE ADVANCED 2015 PAPER 1 OFFLINE20151View paper
JEE ADVANCED 2015 PAPER 2 OFFLINE20152View paper
JEE ADVANCED 2013 PAPER 1 OFFLINE20131View paper
IIT JEE 2012 PAPER 1 OFFLINE20121View paper
IIT JEE 2011 PAPER 1 OFFLINE20111View paper
IIT JEE 2011 PAPER 2 OFFLINE20111View paper
IIT JEE 2010 PAPER 1 OFFLINE20101View paper
IIT JEE 2010 PAPER 2 OFFLINE20101View paper
IIT JEE 2009 PAPER 1 OFFLINE20092View paper
IIT JEE 2008 PAPER 1 OFFLINE20081View paper
IIT JEE 2008 PAPER 2 OFFLINE20081View paper
IIT JEE 200620064View paper
IIT JEE 200520052View paper
IIT JEE 2005 MAINS20053View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 2004 SCREENING20041View paper
IIT JEE 2003 SCREENING20031View paper
IIT JEE 200220021View paper
IIT JEE 2002 SCREENING20022View paper
IIT JEE 200120011View paper
IIT JEE 199919992View paper
IIT JEE 199719972View paper
IIT JEE 199619961View paper
IIT JEE 199519951View paper
IIT JEE 199419941View paper
IIT JEE 199219921View paper
IIT JEE 199119912View 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 198219822View 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
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2
1982 · Mathematics · Calculus · Application Of Integration
IIT JEE 1982
For any real \(t,\,x = {{{e^t} + {e^{ - t}}} \over 2},\,\,y = {{{e^t} - {e^{ - t}}} \over 2}\) is a point on the
hyperbola \({x^2} - {y^2} = 1\). Show that the area bounded by this hyperbola and the lines joining its centre to the points corresponding to \({t_1}\) and \(-{t_1}\) is \({t_1}\).
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3
1982 · Mathematics · Calculus · Application Of Integration
IIT JEE 1982
The area bounded by the curves \(y=f(x)\), the \(x\)-axis and the ordinates \(x=1\) and \(x=b\) is \((b-1)\) sin \((3b+4)\). Then \(f(x)\) is
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4
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 \(a\).
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5
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 \(y = \tan x, - {\pi \over 3} \le x \le {\pi \over 3};\,\,y = \cot x,{\pi \over 6} \le x \le {{3\pi } \over 2}\)
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6
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.
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7
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.
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8
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.
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9
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 \(ln\) \(e=1.\)
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10
1991 · Mathematics · Calculus · Application Of Integration
IIT JEE 1991
If \('f\) is a continuous function with \(\int\limits_0^x {f\left( t \right)dt \to \infty }\) as \(\left| x \right| \to \infty ,\) then show that every line \(y=mx\) IIT-JEE 1991 Mathematics - Application of Integration Question 24 English
intersects the curve \({y^2} + \int\limits_0^x {f\left( t \right)dt = 2!}\)
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11
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.
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12
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.
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13
1994 · Mathematics · Calculus · Application Of Integration
IIT JEE 1994
In what ratio does the \(x\)-axis divide the area of the region
bounded by the parabolas \(y = 4x - {x^2}\) and \(y = {x^2} - x?\)
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14
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.
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15
1996 · Mathematics · Calculus · Application Of Integration
IIT JEE 1996
Let \({A_n}\) be the area bounded by the curve \(y = {\left( {\tan x} \right)^n}\) and the
lines \(x=0,\) \(y=0,\) and \(x = {\pi \over 4}.\) Prove that for \(n > 2,\)
\({A_n} + {A_{n - 2}} = {1 \over {n - 1}}\) and deduce \({1 \over {2n + 2}} < {A_n} < {1 \over {2n - 2}}.\)
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16
1997 · Mathematics · Calculus · Application Of Integration
IIT JEE 1997
If \(g\left( x \right) = \int_0^x {{{\cos }^4}t\,dt,}\) then \(g\left( {x + \pi } \right)\) equals
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17
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 \(x=1.\)
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18
1999 · Mathematics · Calculus · Application Of Integration
IIT JEE 1999
For which of the following values of \(m\), is the area of the region bounded by the curve \(y = x - {x^2}\) and the line \(y=mx\) equals \(9/2\)?
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19
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 \(8x+1=0.\)

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20
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 \(b = \pi .\)
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Showing 20 of 65 questions