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Previous year question hub

Indefinite Integrals - Calculus - Mathematics Previous Year Questions

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

21Papers
21Years
21Questions
1Topics

Indefinite Integrals question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Indefinite Integrals. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 12 57.1%
Hard 5 23.8%
Easy 2 9.5%
Not classified 2 9.5%

Question type distribution

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

Subjective 14 66.7%
MCQ 6 28.6%
Fill in the blanks 1 4.8%

Subject weightage

Top subjects by unique question coverage.

Mathematics
21 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
21 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Indefinite Integrals
21 Qs

Paper coverage

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

IIT JEE 2012 PAPER 1 OFFLINE
1 Qs
IIT JEE 2008 PAPER 2 OFFLINE
1 Qs
IIT JEE 2007 PAPER 2 OFFLINE
1 Qs
IIT JEE 2006
1 Qs
IIT JEE 2005 SCREENING
1 Qs
IIT JEE 2002
1 Qs
IIT JEE 2001
1 Qs
IIT JEE 1999
1 Qs
IIT JEE 1996
1 Qs
IIT JEE 1995 SCREENING
1 Qs
IIT JEE 1994
1 Qs
IIT JEE 1992
1 Qs
IIT JEE 1990
1 Qs
IIT JEE 1989
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
IIT JEE 1979
1 Qs
IIT JEE 1978
1 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
IIT JEE 2012 PAPER 1 OFFLINE20121View paper
IIT JEE 2008 PAPER 2 OFFLINE20081View paper
IIT JEE 2007 PAPER 2 OFFLINE20071View paper
IIT JEE 200620061View paper
IIT JEE 2005 SCREENING20051View paper
IIT JEE 200220021View paper
IIT JEE 200120011View paper
IIT JEE 199919991View paper
IIT JEE 199619961View paper
IIT JEE 1995 SCREENING19951View paper
IIT JEE 199419941View paper
IIT JEE 199219921View paper
IIT JEE 199019901View paper
IIT JEE 198919891View paper
IIT JEE 198719871View paper
IIT JEE 198519851View paper
IIT JEE 198419841View paper
IIT JEE 198319831View paper
IIT JEE 198119811View paper
IIT JEE 197919791View paper
IIT JEE 197819781View paper

All Indefinite Integrals previous year questions

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

1
1978 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1978
Evaluate \(\int {{{\sin x} \over {\sin x - \cos x}}dx}\)
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2
1979 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1979
Evaluate \(\int {{{{x^2}dx} \over {{{\left( {a + bx} \right)}^2}}}}\)
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3
1981 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1981
Evaluate \(\int {\left( {{e^{\log x}} + \sin x} \right)\cos x\,\,dx.}\)
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4
1983 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1983
Evaluate : \(\int {{{\left( {x - 1} \right){e^x}} \over {{{\left( {x + 1} \right)}^3}}}dx}\)
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5
1984 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1984
Evaluate the following \(\int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{3/4}}}}}\)
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6
1985 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1985
Evaluate the following \(\int {\sqrt {{{1 - \sqrt x } \over {1 + \sqrt x }}dx} }\)
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7
1987 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1987
Evaluate :\(\,\,\int {\left[ {{{{{\left( {\cos 2x} \right)}^{1/2}}} \over {\sin x}}} \right]dx}\)
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8
1989 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1989
Evaluate \(\int {\left( {\sqrt {\tan x} + \sqrt {\cot x} } \right)dx}\)
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9
1990 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1990
If \(\int {{{4{e^x} + 6{e^{ - x}}} \over {9{e^x} - 4{e^{ - x}}}}\,dx = Ax + B\,\,\log \left( {9{e^{2x}} - 4} \right) + C,}\) then
\(A = .....,B = .....\) and \(C = .....\)
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10
1992 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1992
Find the indefinite integral \(\int {\left( {{1 \over {\root 3 \of x + \root 4 \of 4 }} + {{In\left( {1 + \root 6 \of x } \right)} \over {\root 3 \of x + \root \, \of x }}} \right)} dx\)
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11
1994 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1994
Find the indefinite integral \(\,\int {\cos 2\theta {\mkern 1mu} ln\left( {{{\cos \theta + \sin \theta } \over {\cos \theta - \sin \theta }}} \right)} {\mkern 1mu} d\theta\)
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12
1995 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1995 SCREENING
The value of the integral \(\int {{{{{\cos }^3}x + {{\cos }^5}x} \over {{{\sin }^2}x + {{\sin }^4}x}}} \,dx\,\) is
Open complete paper
13
1996 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1996
Evaluate \(\int {{{\left( {x + 1} \right)} \over {x{{\left( {1 + x{e^x}} \right)}^2}}}dx}\).
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14
1999 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 1999
Integrate \(\int {{{{x^3} + 3x + 2} \over {{{\left( {{x^2} + 1} \right)}^2}\left( {x + 1} \right)}}dx.}\)
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15
2001 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 2001
Evaluate \(\int {{{\sin }^{ - 1}}\left( {{{2x + 2} \over {\sqrt {4{x^2} + 8x + 13} }}} \right)} \,dx.\)
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16
2002 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 2002
For any natural number \(m\), evaluate
$$\int {\left( {{x^{3m}} + {x^{2m}} + {x^m}} \right){{\left( {2{x^{2m}} + 3{x^m} + 6} \right)}^{l/m}}dx,x > 0.}$$
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17
2005 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 2005 SCREENING
If \(\int\limits_{\sin x}^1 {{t^2}f\left( t \right)dt = 1 - \sin x,}\) then f\(\left( {{1 \over {\sqrt 3 }}} \right)\) is
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18
2006 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 2006

$\int \frac{x^2-1}{x^3 \sqrt{2 x^4-2 x^2+1}} d x$ is equal to

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19
2007 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 2007 PAPER 2 OFFLINE

Let \(f(x)=\frac{x}{\left(1+x^{n}\right)^{1 / n}}\) for \(n \geq 2\) and \(g(x)=\underbrace{(f o f o \ldots . o f)}_{f \text { occurs } n \text { times }}(x)\). Then \(\int x^{n-2} g(x) d x\) equals :

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20
2008 · Mathematics · Calculus · Indefinite Integrals
IIT JEE 2008 PAPER 2 OFFLINE
Let \(I = \int {{{{e^x}} \over {{e^{4x}} + {e^{2x}} + 1}}dx,\,\,J = \int {{{{e^{ - x}}} \over {{e^{ - 4x}} + {e^{ - 2x}} + 1}}dx.} }\) Then

for an arbitrary constant \(C\), the value of \(J -I\) equals :
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Showing 20 of 21 questions