Definite Integration PYQs - Last 10 Years

AP EAPCET / Mathematics / Calculus / 91 recent questions

MathematicsCalculus2016-2025

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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.

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2021-2025

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Last 10 Years Definite Integration Questions

Showing 50 of 91 filtered questions.

1Definite Integration

$$ \lim _{n \rightarrow \infty}\left[\begin{array}{c} \frac{1}{n^2} \sec ^2 \frac{1}{n^2}+\frac{2}{n^2} \sec ^2 \frac{4}{n^2}+\frac{3}{n^2} \sec ^2 \\ \frac{9}{n^2}+\ldots+\frac{1}{n^2} \sec ^2 1 \end{array}\right]= $$

2Definite Integration

\(\int_0^1 x^{\frac{5}{2}}(1-x)^{\frac{3}{2}} d x=\)

3Definite Integration

\(\int_0^1 \frac{2 x+5}{x^2+3 x+2} d x=\)

4Definite Integration

If $f(x)=\max \left\{x^3-4, x^4-4\right\}$ and $g(x)=\min \left\{x^2, x^3\right\}$, then $\int_{-1}^1(f(x)-g(x)) d x=$

5Definite Integration

\(\int_0^2 x^2(2-x)^5 d x=\)

6Definite Integration

\(\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin (x-[x]) d x=\)
Here $[x]$ is the greatest integer function

7Definite Integration

\(\int_0^1 x \sin ^{-1} x d x=\)

8Definite Integration

\(\int_0^1 \frac{x^4+1}{x^6+1} d x=\)

9Definite Integration

\(\int_0^\pi\left(\sin ^5 x \cos ^3 x+\sin ^4 x \cos ^4 x+\sin ^3 x \cos ^4 x\right) d x=\)

10Definite Integration

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

11Definite Integration

\(\int_0^2 x^8\left(\frac{4}{x^2}-1\right)^{\frac{5}{2}} d x=\)

12Definite Integration

If $f(t)=\int_0^t \tan ^{(2 n-1)} x d x, n \in N$, then $f(t+\pi)=$

13Definite Integration

\(\int_{\frac{5}{6}}^\pi \cos ^{-4} x d x=\)

14Definite Integration

\(\int\limits_0^{\frac{3 \pi}{2}} \frac{\cos ^3 x}{\cos ^3 x+\sin ^3 x} d x=\)

15Definite Integration

\(\int_0^x \frac{t^2}{\sqrt{a^2+t^2}} d t=\)

16Definite Integration

\(\int_{1 / 5}^{1 / 2} \frac{\sqrt{x-x^2}}{x^3} d x=\)

17Definite Integration

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

18Definite Integration

\(\int_0^{400 \pi} \sqrt{1-\cos 2 x} d x=\)

19Definite Integration

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

20Definite Integration

$\int_{\frac{-\pi}{4}}^{\frac{\pi}{3}}\left|\tan \left(x-\frac{\pi}{6}\right)\right| d x=$

21Definite Integration

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

22Definite Integration

\(\int_{5 \pi}^{25 \pi}|\sin 2 x+\cos 2 x| d x=\)

23Definite Integration

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

24Definite Integration

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

25Definite Integration

If $k \in N$, then $\lim\limits_{n \rightarrow \infty}\left[\frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\ldots .+\frac{1}{k n}\right]=$

26Definite Integration

\(\int_0^{\frac{\pi}{2}} \log |\tan x+\cot x| d x=\)

27Definite Integration

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

28Definite Integration

\(\int_0^\pi x \cdot \sin ^5 x \cdot \cos ^6 x d x=\)

29Definite Integration

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

30Definite Integration

Let $H(x)=3 x^4+6 x^3-2 x^2+1$ and $g(x)$ be a linear polynomial. If $\frac{H(x)}{(x-1)(x+1)(x-2)}=f(x) +\frac{g(x)}{(x-1)(x+1)(x-2)}$, then
$H(-1)+2 H(2)-3 H(1)=$

31Definite Integration

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

32Definite Integration

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

33Definite Integration

If $A=\int_0^{\infty} \frac{1+x^2}{1+x^4} d x, B=\int_0^1 \frac{1+x^2}{1+x^4} d x$, then

34Definite Integration

If $\int_0^{2 \pi}\left(\sin ^4 x+\cos ^4 x\right) d x=K \int_0^\pi \sin ^2 x d x+L \int_0^{\frac{\pi}{2}} \cos ^2 x d x$ and $K, L \in N$, then the number of possible ordered pairs ( $K, L$ ) is

35Definite Integration

$\int_0^\pi \frac{x \sin x}{4 \cos ^2 x+3 \sin ^2 x} d x$ is equal to

36Definite Integration

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

37Definite Integration

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

38Definite Integration

\(\mathop {\lim }\limits_{x \to \infty }\left[\left(1+\frac{1}{n^3}\right)^{\frac{1}{n^3}}\left(1+\frac{8}{n^3}\right)^{\frac{4}{n^3}}\left(1+\frac{27}{n^3}\right)^{\frac{9}{n^3}} \ldots . .(2)^{\frac{1}{n}}\right] \text { is equaln }\)

39Definite Integration

$\int_0^1 \sqrt{\frac{2+x}{2-x}} d x$ is equal to

40Definite Integration

$\int\limits_{-5 \pi}^{5 \pi}(1-\cos 2 x)^{\frac{5}{2}} d x$ is equal to

41Definite Integration

$\int\limits_{-2}^2\left(4-x^2\right)^{\frac{5}{2}} d x$ is equal to

42Definite Integration

If $M=\int\limits_0^{\infty} \frac{\log t}{1+t^3} d t$ and $N=\int\limits_{-\infty}^{\infty} \frac{t e^{2 t}}{1+e^{3 t}} d t$, then

43Definite Integration

If $\int_1^n[x] d x=120$, then $n=$

44Definite Integration

$$ \text { If } f(x)=\left\{\begin{array}{cc} \frac{6 x^2+1}{4 x^3+2 x+3} & , 0 < x < 1 \\ x^2+1 & , 1 \leq x < 2 \end{array} \text {, then } \int_0^2 f(x) d x=\right. $$

45Definite Integration

If $729 \int_1^3 \frac{1}{x^3\left(x^2+9\right)^2} d x=a+\log b$, then $(a-b)=$

46Definite Integration

$\lim \limits_{n \rightarrow \infty} \frac{1^{17}+2^{77}+\ldots+n^{77}}{n^{78}}=$

47Definite Integration

\(\int_{-1}^1\left(\sqrt{1+x+x^2}-\sqrt{1-x+x^2}\right) d x=\)

48Definite Integration

$\int_0^1 \frac{x}{(1-x)^{\frac{3}{4}}} d x=$

49Definite Integration

$\int_1^5(|x-3|+|1-x|) d x=$

50Definite Integration

\(\int\limits_0^{\pi /4} {{{{x^2}} \over {{{(x\,\sin \,x + \cos \,x)}^2}}}dx = }\)