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Previous year question hub

Indefinite Integration - Calculus - Mathematics Previous Year Questions

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

14Papers
3Years
63Questions
1Topics

Indefinite Integration question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 63 100%

Question type distribution

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

Multiple Choices 63 100%

Subject weightage

Top subjects by unique question coverage.

Mathematics
63 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
63 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Indefinite Integration
63 Qs

Paper coverage

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

TS EAMCET 2023 (Online) 12th May Morning Shift
6 Qs
TS EAMCET 2023 ONLINE 12TH MAY EVENING SHIFT
4 Qs
TS EAMCET 2023 ONLINE 13TH MAY EVENING SHIFT
4 Qs
TS EAMCET 2023 ONLINE 13TH MAY MORNING SHIFT
4 Qs
TS EAMCET 2023 ONLINE 14TH MAY EVENING SHIFT
4 Qs
TS EAMCET 2023 ONLINE 14TH MAY MORNING SHIFT
4 Qs
TS EAMCET 2022 (Online) 20th July Evening Shift
5 Qs
TS EAMCET 2022 (Online) 20th July Morning Shift
5 Qs
TS EAMCET 2022 ONLINE 18TH JULY MORNING SHIFT
5 Qs
TS EAMCET 2022 (Online) 19th July Evening Shift
4 Qs
TS EAMCET 2022 (Online) 19th July Morning Shift
4 Qs
TS EAMCET 2022 ONLINE 18TH JULY EVENING SHIFT
4 Qs
TS EAMCET 2020 (Online) 10th September Evening Shift
5 Qs
TS EAMCET 2020 (Online) 10th September Morning Shift
5 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
TS EAMCET 2023 (Online) 12th May Morning Shift20236View paper
TS EAMCET 2023 ONLINE 12TH MAY EVENING SHIFT20234View paper
TS EAMCET 2023 ONLINE 13TH MAY EVENING SHIFT20234View paper
TS EAMCET 2023 ONLINE 13TH MAY MORNING SHIFT20234View paper
TS EAMCET 2023 ONLINE 14TH MAY EVENING SHIFT20234View paper
TS EAMCET 2023 ONLINE 14TH MAY MORNING SHIFT20234View paper
TS EAMCET 2022 (Online) 19th July Evening Shift20224View paper
TS EAMCET 2022 (Online) 19th July Morning Shift20224View paper
TS EAMCET 2022 (Online) 20th July Evening Shift20225View paper
TS EAMCET 2022 (Online) 20th July Morning Shift20225View paper
TS EAMCET 2022 ONLINE 18TH JULY EVENING SHIFT20224View paper
TS EAMCET 2022 ONLINE 18TH JULY MORNING SHIFT20225View paper
TS EAMCET 2020 (Online) 10th September Evening Shift20205View paper
TS EAMCET 2020 (Online) 10th September Morning Shift20205View paper

All Indefinite Integration previous year questions

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

1
2022 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2022 ONLINE 18TH JULY EVENING SHIFT

$$\begin{aligned} & \text { If } \int \frac{(x+3)}{(x-1)^2(2 x-1)} d x \\ & =\frac{A}{x-1}+B \log (2 x-1)+C \log (x-1)+k, \text { then } A+B+C= \end{aligned}$$

A

3

B

11

C

-4

D

-11

Open complete paper
2
2022 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2022 ONLINE 18TH JULY EVENING SHIFT

Let $x \neq \frac{-3}{5}, \frac{2}{5}$, if $f\left(\frac{2 x+1}{5 x+3}\right)=x+2$, then $\int f(x) d x=$

A

$\frac{7}{5} x-\frac{1}{5} \log |5 x+3|+c$

B

$\frac{7}{5} x-\frac{1}{25} \log |5 x+3|+c$

C

$\frac{7}{5} x-\frac{1}{25} \log |5 x-2|+c$

D

$\frac{7}{5} x-\frac{1}{5} \log |5 x-2|+c$

Open complete paper
3
2022 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2022 ONLINE 18TH JULY EVENING SHIFT

If $\int \frac{1+\cos 8 x}{\tan 2 x-\cot 2 x} d x=f(x) \cdot \cos (g(x))+c$, then $f\left(\frac{1}{4}\right)+g\left(\frac{1}{4}\right)=$

A

2

B

$\frac{17}{8}$

C

$\frac{15}{8}$

D

$\frac{33}{16}$

Open complete paper
4
2022 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2022 ONLINE 18TH JULY EVENING SHIFT

If $\int e^x \cos x d x=\frac{e^x}{2}(\cos x+\sin x)$ and

$$\int \frac{\cos \left(\log \left(\frac{2 x+3}{3-2 x}\right)\right)}{(3-2 x)^2} d x=\frac{f(x)}{24}[\cos (g(x))+\sin (g(x))]+c$$

then $g(1)=$

A

5

B

$\log f(2)$

C

$\log f(1)$

D

0

Open complete paper
5
2022 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2022 ONLINE 18TH JULY MORNING SHIFT

If $x>0$ and $x \neq(2 n+1) \frac{\pi}{2}$, then $\int\left(x \sqrt{x}-e^{\log (\sec x \tan x)}+\frac{3 x^2-2 x+1}{x^2}\right) d x=$

A

$x \sqrt{x}-\sec x+3 x-2 \log x-\frac{1}{x}+c$

B

$\frac{2}{5} x^2 \sqrt{x}-\sec x+3 x+\frac{2}{x^2}-\frac{1}{x}+c$

C

$x \sqrt{x}-\sec x+3 x+\frac{2}{x^2}-\frac{1}{x}+c$

D

$\frac{2}{5} x^2 \sqrt{x}-\sec x+3 x-2 \log x-\frac{1}{x}+c$

Open complete paper
6
2022 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2022 ONLINE 18TH JULY MORNING SHIFT

Let $f(x)=\int \frac{2 x^3-3 x^2+4 x-5}{x^2} d x$ and $f(1)=1$. Then, $f(5)=$

A

$10+4 \log 5$

B

$10-4 \log 5$

C

$9+4 \log 5$

D

$9-4 \log 5$

Open complete paper
7
2022 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2022 ONLINE 18TH JULY MORNING SHIFT

If $\frac{x^2+3}{\left(x^2+1\right)\left(x^2+2\right)}=\frac{A x+B}{x^2+1}+\frac{C x+D}{x^2+2}$ then $A+B+C+D=$

A

3

B

2

C

0

D

1

Open complete paper
8
2022 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2022 ONLINE 18TH JULY MORNING SHIFT

If $\frac{x^2-3 x+2}{(x-4)(x-3)^2}=\frac{A}{x-4}+\frac{B}{x-3}+\frac{C}{(x-3)^2}$ then $A+B+C=$

A

1

B

0

C

-1

D

5

Open complete paper
9
2022 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2022 ONLINE 18TH JULY MORNING SHIFT

$$\int(2 x-3) \sqrt{3 x+2} d x=$$

A

$\frac{2}{135}\left(54 x^2-123 x+106\right) \sqrt{3 x+2}+c$

B

$\frac{2}{135}\left(54 x^2+123 x-106\right) \sqrt{3 x+2}+c$

C

$\frac{2}{135}\left(54 x^2-123 x-106\right) \sqrt{3 x+2}+c$

D

$\frac{2}{135}\left(54 x^2-195 x-106\right) \sqrt{3 x+2}+c$

Open complete paper
10
2023 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2023 ONLINE 12TH MAY EVENING SHIFT
$$\text { Match the following items from List I into List II }$$
List-I List-II
1. \(\int \frac{\mathrm{sin}^{2} x}{\mathrm{cos}^{4} x} d x\)\(\int \frac{\mathrm{sin}^{2} x}{\mathrm{cos}^{4} x} d x\)int(sin^(2)x)/(cos^(4)x)dx A. \(\quad \frac{\mathrm{tan}^{2} x}{2} + \mathrm{ln} | \mathrm{cos} x | + C\)\(\quad \frac{\mathrm{tan}^{2} x}{2} + \mathrm{ln} | \mathrm{cos} x | + C\)quad(tan^(2)x)/(2)+ln |cos x|+C
2. \(\int \frac{\mathrm{sin}^{4} x}{\mathrm{cos}^{2} x} d x\)\(\int \frac{\mathrm{sin}^{4} x}{\mathrm{cos}^{2} x} d x\)int(sin^(4)x)/(cos^(2)x)dx B. \(\mathrm{cos} x + \mathrm{sec} x + C\)\(\mathrm{cos} x + \mathrm{sec} x + C\)cos x+sec x+C
3. \(\int \frac{\mathrm{sin}^{3} x}{\mathrm{cos}^{2} x} d x\)\(\int \frac{\mathrm{sin}^{3} x}{\mathrm{cos}^{2} x} d x\)int(sin^(3)x)/(cos^(2)x)dx C. \(\frac{\mathrm{tan}^{3} x}{3} + C\)\(\frac{\mathrm{tan}^{3} x}{3} + C\)(tan^(3)x)/(3)+C
4. \(\int \frac{\mathrm{sin}^{3} x}{\mathrm{cos}^{3} x} d x\)\(\int \frac{\mathrm{sin}^{3} x}{\mathrm{cos}^{3} x} d x\)int(sin^(3)x)/(cos^(3)x)dx D. \(\mathrm{tan} x + \frac{\mathrm{sin} 2 x}{4} - \frac{3 x}{2} + C\)\(\mathrm{tan} x + \frac{\mathrm{sin} 2 x}{4} - \frac{3 x}{2} + C\)tan x+(sin 2x)/(4)-(3x)/(2)+C
E. \(\mathrm{cos} x - \mathrm{sec} x + C\)\(\mathrm{cos} x - \mathrm{sec} x + C\)cos x-sec x+C
Select the correct choice
A
1-C, 2-E, 3-B, 4-A
B
1,-C, 2-D, 3-B, 4-A
C
1-D, 2-C, 3-A, 4-B
D
1-C, 2-E, 3-A, 4-D
Open complete paper
11
2023 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2023 ONLINE 12TH MAY EVENING SHIFT

If $\int x^4(\log x)^3 d x=x^5\left[A(\log x)^3\right]$ $\left.+B(\log x)^2+C \log x+D\right]+k$, then $A+B+C+5 D=$

A
$\frac{2}{25}$
B
$\frac{8}{25}$
C
$\frac{12}{125}$
D
$\frac{16}{125}$
Open complete paper
12
2023 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2023 ONLINE 12TH MAY EVENING SHIFT
If $\int \frac{x}{(a+x)^5} d x=\frac{1}{k(a+x)^4}(f(x))+C$, then $\frac{f(-a)}{a k}=$
A
$1 / 3$
B
$1 / 2$
C
$5 / 6$
D
$1 / 4$
Open complete paper
13
2023 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2023 ONLINE 12TH MAY EVENING SHIFT

If $\frac{x+1}{\left(x^2+1\right)(x-1)^2}=\frac{A x+B}{x^2+1}+\frac{C}{x-1}+\frac{D}{(x-1)^2}$, then $A+B+C+D=$

A
$-\frac{1}{2}$
B
$\frac{1}{2}$
C
1
D
$\frac{3}{2}$
Open complete paper
14
2023 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2023 ONLINE 13TH MAY EVENING SHIFT

If $\int \frac{2 \sin 2 x-3 \cos x}{2 \sin ^2 x-3 \sin x+4} d x=f(x)+C$, where $C$ is the constant of integration, then $f\left(\frac{\pi}{2}\right)-f(0)=$

A

$2 \log 2$

B

0

C

$\log \left(\frac{3}{4}\right)$

D

1

Open complete paper
15
2023 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2023 ONLINE 13TH MAY EVENING SHIFT

$\int \frac{1}{\left(x+\frac{2}{x}\right) \sqrt{x^4+4 x^2+3}} d x=$

A

$\frac{1}{2} \sec ^{-1}\left(x^2+2\right)+C$

B

$-\operatorname{cosech}^{-1}\left(x^2+2\right)+C$

C

$\frac{1}{2} \tan ^{-1}\left(x+\frac{2}{x}\right)+C$

D

$-\frac{1}{2} \cot ^{-1}\left(x+\frac{2}{x}\right)+C$

Open complete paper
16
2023 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2023 ONLINE 13TH MAY EVENING SHIFT

If $\frac{3 \pi}{2} < x < \frac{5 \pi}{2}$ and $\int(\sqrt{1-\sin x}+\sqrt{1+\sin x}) d x=f(x)+C$, where $C$ is the constant of integration, then $f\left(\frac{\pi}{3}\right)-f(0)=$

A

2

B

-2

C

$2 \sqrt{2}$

D

$-2 \sqrt{2}$

Open complete paper
17
2023 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2023 ONLINE 13TH MAY EVENING SHIFT

$\int \frac{2 x+3}{\sqrt{3 x^2-2 x+1}} d x=$

A

$\frac{2}{3} \sqrt{3 x^2-2 x+1}+\frac{11}{3} \sinh ^{-1}\left(\frac{3 x-1}{\sqrt{2}}\right)+C$

B

$\frac{1}{3} \sqrt{3 x^2-2 x+1}+\frac{11}{3} \sinh ^{-1}\left(\frac{\sqrt{3} x-1}{\sqrt{2}}\right)+C$

C

$\frac{1}{3} \sqrt{3 x^2-2 x+1}+\frac{11}{3} \sinh ^{-1}\left(\frac{3 x-1}{\sqrt{3}}\right)+C$

D

$\frac{2}{3} \sqrt{3 x^2-2 x+1}+\frac{11}{3 \sqrt{3}} \sinh ^{-1}\left(\frac{3 x-1}{\sqrt{2}}\right)+C$

Open complete paper
18
2023 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2023 ONLINE 13TH MAY MORNING SHIFT

$$\int \frac{1}{16-7 \sin ^2 x} d x=$$

A

$\frac{1}{12} \tan ^{-1}\left(\frac{3 \tan x}{4}\right)+C$

B

$\frac{1}{3} \sin ^{-1}\left(\frac{3 \sin x}{4}\right)+C$

C

$\frac{1}{12} \log \left(\frac{4-\sqrt{7} \sin x}{4+\sqrt{7} \sin x}\right)+C$

D

$\frac{1}{12} \log \left(\frac{4+\sqrt{7} \sin x}{4-\sqrt{7} \sin x}\right)+C$

Open complete paper
19
2023 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2023 ONLINE 13TH MAY MORNING SHIFT

$$\int \frac{1}{(x-2)\left(x^2+1\right)} d x=$$

A

$\log \frac{\sqrt{x^2+1}}{|x-2|}+2 \tan ^{-1} x+C$

B

$\log \frac{|x-2|}{x^2+1}+2 \tan ^{-1} x+C$

C

$\frac{1}{5}\left[\log \frac{|x-2|}{\sqrt{7+x^2}}+2 \tan ^{-1} x\right]+C$

D

$\frac{1}{5}\left[\log \frac{|x-2|}{\sqrt{1+x^2}}-2 \tan ^{-1} x\right]+C$

Open complete paper
20
2023 · Mathematics · Calculus · Indefinite Integration
TS EAMCET 2023 ONLINE 13TH MAY MORNING SHIFT

$$\int \frac{\sec ^2 x}{(\sec x+\tan x)^2} d x=$$

A

$\frac{3+(\sec x+\tan x)^2}{2(\sec x+\tan x)^3}+C$

B

$-\frac{1+3(\sec x+\tan x)^2}{6(\sec x+\tan x)^3}+C$

C

$-\frac{3+(\sec x+\tan x)^2}{2(\sec x+\tan x)^3}+C$

D

$-\frac{1+(\sec x+\tan x)}{3(\sec x+\tan x)^2}+C$

Open complete paper

Showing 20 of 63 questions