Definite Integration PYQs - Last 10 Years

TS EAMCET / Mathematics / Calculus / 74 recent questions

MathematicsCalculus2016-2025

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Practice 74 TS EAMCET Mathematics questions from Definite Integration. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

74

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Mathematics / Calculus

2020-2025

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60

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2021-2025

74

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2016-2025

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60 in last 5 years74 in last 10 years

Last 10 Years Definite Integration Questions

Showing 50 of 74 filtered questions.

1Definite Integration

\(\int_0^{\frac{\pi}{2}} \frac{d x}{\cos x-\sqrt{3} \sin x}=\)

2Definite Integration

\(\int_{-4}^5 \frac{1}{\sqrt{20+x-x^2}} d x=\)

3Definite Integration

\(\int_0^{\frac{\pi}{2}} \sqrt{\tan x d x}=\)

4Definite Integration

\(\lim _{n \rightarrow \infty} \frac{\left(2 n(2 n-1) \ldots .(n+2)(n+1)^{1 / n}\right.}{n}=\)

5Definite Integration

If $\int_0^{\frac{\pi}{2}} \tan ^{14}\left(\frac{x}{2}\right) d x=2\left[\sum_{n=1}^7 f(n)-\frac{\pi}{4}\right]$, then $f(n)=$

6Definite Integration

If [.] denotes the greatest integer function, then $\int_1^2\left[x^2\right] d x=$

7Definite Integration

\(\int_8^{18} \frac{1}{(x+2) \sqrt{x-3}} d x=\)

8Definite Integration

\(\int_0^{\pi / 4} \frac{1}{5 \cos ^2 x+16 \sin ^2 x+8 \sin x \cos x} d x=\)

9Definite Integration

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

10Definite Integration

\(\int_{-2}^4\left|2-x^2\right| d x=\)

11Definite Integration

\(\int_{-1}^1 \frac{\log 2-\log (1+x)}{\sqrt{1-x^2}} d x=\)

12Definite Integration

\(\int_{-2 \pi}^{2 \pi} \sin ^4 x \cos ^6 x d x=\)

13Definite Integration

\(\int_0^{\pi / 4} x^2 \sin 2 x d x\)

14Definite Integration

\(\int_0^2 \sqrt{(x+3)(2-x)} d x=\)

15Definite Integration

\(\mathop {\lim }\limits_{n \to \infty } \frac{1}{n^2}\left[e^{1 / n}+2 e^{2 / n}+3 e^{3 / n}+\ldots+2 n e^2\right]=\)

16Definite Integration

Let $m, n, p, q$ be four positive integers. If
$$ \begin{aligned} & \int_0^{2 \pi} \sin ^m x \cos ^n x d x=4 \int_0^{\pi / 2} \sin ^m x \cos ^n x d x \int_0^{2 \pi} \sin ^p x \cos ^n x d x=0 \\ & \int_0^\pi \sin ^p x \cos ^q x d x=0, a=m+n+...

17Definite Integration

$\int_{-2}^2 x^4\left(4-x^2\right)^{\frac{7}{2}} d x=$

18Definite Integration

If $f(x)=\int \frac{\sin 2 x+2 \cos x}{4 \sin ^2 x+5 \sin x+1} d x$ and $f(0)=0$, then $f(\pi / 6)=$

19Definite Integration

$\int_0^{32 \pi} \sqrt{1-\cos 4 x} d x=$

20Definite Integration

$\int_0^{16} \frac{\sqrt{x}}{1+\sqrt{x}} d x=$

21Definite Integration

$ \int_{\frac{-3}{4}}^{\frac{\pi-6}{8}} \log (\sin (4 x+3)) d x= $

22Definite Integration

$\int_{-\pi / 15}^{\pi / 5} \frac{\cos 5 x}{1+e^{5 x}} d x=$

23Definite Integration

$\int_{\frac{\pi}{5}}^{\frac{3 \pi}{10}} \frac{d x}{\sec ^{2} x+\left(\tan ^{2024} x-1\right)\left(\sec ^{2} x-1\right)}=$

24Definite Integration

$\int_{\frac{-\pi}{8}}^{\frac{\pi}{8}} \frac{\sin ^4(4 x)}{1+e^{4 x}} d x=$

25Definite Integration

$\int_0^\pi\left(\sin ^3 x+\cos ^2 x\right)^2 d x=$

26Definite Integration

$\frac{3}{25} \int_{0}^{25 \pi} \sqrt{\left|\cos x-\cos ^{3} x\right|} d x=$

27Definite Integration

If $m, l, r, s, n$ are integers such that $9 > m > l > s > n > r > 2$ and $\int_{-2 \pi}^{2 \pi} \sin ^{m} x \cos ^{n} x d x=4 \int_{0}^{\pi} \sin ^{m} x \cos ^{n} x d x, \int_{-\pi}^{\pi} \sin ^{r} x \cos ^{s} x d x$ $=4 \int_{0}^{\pi / 2}...

28Definite Integration

\(\int_{-\pi / 2}^{\pi / 2} \sin ^2 x \cos ^2 x(\sin x+\cos x) d x=\)

29Definite Integration

If $\int_0^3\left(3 x^2-4 x+2\right) d x=k$, then an integer root of $3 x^2-4 x+2=3 k / 5$ is

30Definite Integration

\(\int_{-1}^1 x|x| d x=\)

31Definite Integration

\(\lim _{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{2^2}{n^2}\right) \ldots(2)\right]^{1 / n}=\)

32Definite Integration

\(\int_3^6 \frac{\sqrt{x}}{\sqrt{9-x}+\sqrt{x}} d x=\)

33Definite Integration

\(\int_0^{\pi / 2} \frac{x \tan x \sec ^2 x}{\tan ^4 x+1} d x=\)

34Definite Integration

\(\int_0^3\left|x^2-3 x+2\right| d x=\)

35Definite Integration

\(\int_0^2 x^{\frac{5}{2}} \sqrt{2-x} d x=\)

36Definite Integration

\(\int_{-\frac{\pi}{8092}}^{\frac{\pi}{8092}} \frac{\sec (2023 x)}{1+(2023)^{(2023 x)}} d x=\)

37Definite Integration

If $[x]$ represents greatest integer function, then
\(\int_{-2}^2[2-x] d x=\)

38Definite Integration

\(\int_0^2 \frac{x}{(2-x)^{\frac{3}{4}}} d x=\)

39Definite Integration

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

40Definite Integration

\(\int_0^2 x^3(2-x)^4 d x=\)

41Definite Integration

\(\int_{1 / 2}^2\left|\log _{10} x\right| d x=\)

42Definite Integration

If $f$ is defined on $R$ such that $f(x) f(-x)=9$, then

\(\int_{-23}^{23} \frac{d x}{3+f(x)}=\)

43Definite Integration

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

44Definite Integration

[.] is the greatest integer function, then
\(\int_0^{2 \pi}[|\sin x|+|\cos x|] d x=\)

45Definite Integration

\(\int_0^{\pi / 4} \frac{\sec x}{1+2 \sin ^2 x} d x=\)

46Definite Integration

\(\lim\limits_{n \rightarrow \infty}\left[\frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4}{n^2}+\ldots \ldots+\frac{1}{n} \sec ^2 1\right]=\)

47Definite Integration

\(\int\limits_0^{\frac{\pi}{2}} \sin ^6 x \cos ^4 x d x=\)

48Definite Integration

\(\int\limits_2^5 \sqrt{\frac{5-x}{x-2}} d x=\)

49Definite Integration

Given that $\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{r=1}^{n p} f\left(\frac{r}{n}\right)=\int_0^p f(x) d x$. If $f: R \rightarrow R$ is defined by $f(x)=x^2+2$, then

$$ \lim _{n \rightarrow \infty} \frac{3}{n}\left[f\left(\frac{7}{...

50Definite Integration

If $f(x)=\left|\begin{array}{ccc}2 \cos ^2 x & \sin 2 x & \sin x \\ \sin 2 x & 2 \sin ^2 x & -\cos x \\ \sin x & -\cos x & 0\end{array}\right|$, then
\(\left.\int_0^{\pi / 4}|2| f(x) \mid+5 f^{\prime}(x)\right) d x=\)