Definite Integration PYQs - Last 5 Years

AP EAPCET / Mathematics / Calculus / 91 recent questions

MathematicsCalculus2021-2025

All Definite Integration PYQs Last 10 Years Create chapter test

Practice 91 AP EAPCET Mathematics questions from Definite Integration. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

91

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Mathematics / Calculus

2021-2025

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91

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2021-2025

91

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2016-2025

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91 in last 5 years91 in last 10 years

Last 5 Years Definite Integration Questions

Showing 41 of 91 filtered questions.

1Definite Integration

\(\int_{\frac{1}{\sqrt[5]{31}}}^{\frac{1}{\sqrt[5]{242}}} \frac{1}{\sqrt[5]{x^{30}+x^{25}}} d x=\)

2Definite Integration

$\int_{-\pi}^\pi \frac{x \sin ^3 x}{4-\cos ^2 x} d x=$

3Definite Integration

\(\text { } \int\limits_{-3}^3|2-x| d x=\)

4Definite Integration

$\int_0^\pi \frac{x \sin x}{1+\cos ^2 x} d x=$

5Definite Integration

If $[x]$ is the greatest integer function, then $\int_0^5[x] d x=$

6Definite Integration

$\int\limits_{\frac{-1}{24}}^{\frac{1}{24}} \sec x \log \left(\frac{1-x}{1+x}\right) d x=$

7Definite Integration

$\int_0^{\frac{\pi}{2}} \frac{1}{1+\sqrt{\tan x}} d x=$

8Definite Integration

If $\lim \limits_{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{4}{n^2}\right)\left(1+\frac{9}{n^2}\right) \ldots\left(1+\frac{n^2}{n^2}\right)\right]^{\frac{1}{n}}=a e^b$, then

\(a+b=\)

9Definite Integration

If $I_n=\int_0^{\frac{\pi}{4}} \tan ^n x d x$, then $I_{13}+I_{11}=$

10Definite Integration

\(\int_0^\pi x \sin ^4 x \cos ^6 x d x=\)

11Definite Integration

$\int_1^2 \frac{x^4-1}{x^6-1} d x=$

12Definite Integration

$\int_{\log 4}^{\log 4} \frac{e^{2 x}+e^x}{e^{2 r}-5 e^x+6} d x=$

13Definite Integration

$\lim \limits_{n \rightarrow+\infty}\left[{\frac{1}{n^4}+\frac{1}{\left(n^2+1\right)^{\frac{3}{2}}}+\frac{1}{\left(n^2+4\right)^{\frac{3}{2}}}+\frac{1}{\left(n^2+9\right)^{\frac{3}{2}}}}{+\ldots \ldots+\frac{1}{4 \sqrt{2} n^5}}\right]=$

14Definite Integration

Assertion (A) $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{(\sin x)^{\sqrt{2}} d x}{(\sin x)^{\sqrt{2}}+(\cos x)^{\sqrt{2}}}=\frac{\pi}{12}$
Reason (R) $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{f(x) d x}{f(x)+f\left(\frac{\pi}{2}-x\right)}...

15Definite Integration

If $I=\int_{-a}^a\left(x^4-2 x^2\right) d x$, then $I$ is minimum at $a=$

16Definite Integration

If $[x]$ is the greatest integer not exceeding $x$, then \(\int_{-0.5}^{1.5} x^2[x] d x=\)

17Definite Integration

If $f(x)=\frac{x^3+5}{\sqrt{12+x}}$ and $\int_{-5}^5 f(x) d x=\int_0^5(f(x)+g(x)) d x$, then $g(x)=$

18Definite Integration

\(\int_0^{50 \pi} \sqrt{1-\cos 2 x} d x=\)

19Definite Integration

\(\int_0^{\frac{\pi}{2}}\left(\frac{\sin \left(\frac{\pi}{4}+x\right)+\sin \left(\frac{3 \pi}{4}+x\right)}{\cos x+\sin x}\right) d x=\)

20Definite Integration

\(\int_0^{\frac{\pi}{4}} \frac{\cos ^2 x}{\cos ^2 x+4 \sin ^2 x} d x=\)

21Definite Integration

\(\int_0^1(\sqrt{10})^{2 x} d x=\)

22Definite Integration

If $f(x)=\int_0^x\left[(a+1)(t+1)^2-(a-1)\left(t^2+t+1\right)\right] d t$, then a possible positive value of ' $a$ ', for which $f^{\prime}(x)=0$ has equal roots, is

23Definite Integration

$$\begin{aligned} & \lim _{n \rightarrow \infty}\left[\frac{n}{(n+1) \sqrt{2 n+1}}+\frac{n}{(n+2) \sqrt{2(2 n+2)}}\right. \\ & \left.+\frac{n}{(n+3) \sqrt{3(2 n+3)}}+\ldots n \text { terms }\right]=\int_\limits0^1 f(x) d x \end{aligned}$$
...

24Definite Integration

[ . ] represents greatest integer function, then \(\int_{-1}^1(x[1+\sin \pi x]+1) d x=\)

25Definite Integration

\(\int_\limits1^3 x^n \sqrt{x^2-1} d x=6 \text {, then } n=\)

26Definite Integration

Let \(T>0\) be a fixed number. \(f: R \rightarrow R\) is a continuous function such that \(f(x+T)=f(x), x \in R\)
If \(I=\int_\limits0^T f(x) d x\), then \(\int_\limits0^{5 T} f(2 x) d x=\)

27Definite Integration

Let \(\alpha\) and \(\beta(\alpha<\beta)\) are roots of \(18 x^2-9 \pi x+\pi^2=0, f(x)=x^2, g(x)=\cos x\). Then, \(\int_\alpha^\beta x(g \circ f(x)) d x=\)

28Definite Integration

\(\int_0^1 a^k x^k d x=\)

29Definite Integration

\(\int_0^\pi x\left(\sin ^2(\sin x)+\cos ^2(\cos x)\right) d x=\)

30Definite Integration

\(\int_{\pi / 4}^{5 \pi / 4}(|\cos t| \sin t+|\sin t| \cos t) d t=\)

31Definite Integration

If \(I_n=\int_0^{\pi / 4} \tan ^n x d x\), then \(\frac{1}{I_2+I_4}+\frac{1}{I_3+I_5}+\frac{1}{I_4+I_6}=\)

32Definite Integration

\(\int_0^{\pi / 4} e^{\tan ^2 \theta} \sin ^2 \theta \tan \theta d \theta=\)

33Definite Integration

If \(f(x)=\max \{\sin x, \cos x\}\) and \(g(x)=\min \{\sin x, \cos x\}\), then \(\int_0^\pi f(x) d x+\int_0^\pi g(x) d x=\)

34Definite Integration

\(\int_1^2 {{{{x^3} - 1} \over {{x^2}}}}\) is equal to

35Definite Integration

If \(\int_0^a {{{dx} \over {4 + {x^2}}} = {\pi \over 8}}\), then the value of a is equal to

36Definite Integration

If \(\int_\limits0^1 x^m(1-x)^n d x=k \int_\limits0^1 x^n(1-x)^m d x\), then the value of $k$ equals

37Definite Integration

If \(\int_\limits0^\pi \log (\sin x) d x=8 k\), then \(\int_\limits0^{\frac{\pi}{4}} \log (1+\tan x) d x\) is equal to

38Definite Integration

\(\int\limits_{-1 / 2}^{1 / 2}\left\{[x]+\log \left(\frac{1+x}{1-x}\right)\right\} d x\) is equal to

39Definite Integration

\(\int_2^4\{|x-2|+|x-3|\} d x\) is equal to

40Definite Integration

\(\int_0^2 x e^x d x\) is equal to

41Definite Integration

If \(\int_0^{\pi / 2} \tan ^n(x) d x=k \int_0^{\pi / 2} \cot ^n(x) d x\), then