Definite Integration PYQs - Last 10 Years

MHT CET / Mathematics / Calculus / 146 recent questions

MathematicsCalculus2017-2026

All Definite Integration PYQs Last 5 Years Create chapter test

Practice 146 MHT CET Mathematics questions from Definite Integration. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

146

PYQs on Page

Mathematics / Calculus

2019-2026

Year Range

Based on indexed question metadata

108

Last 5 Years

2022-2026

146

Last 10 Years

2017-2026

Recent Year Trend

2021

2022

2023

2024

2025

2026

202136 max PYQs/year2026

Question Types

146PYQs

MCQ100%

Difficulty Mix

#1 Unknown146

108 in last 5 years146 in last 10 years

Last 10 Years Definite Integration Questions

Showing 50 of 146 filtered questions.

1Definite Integration

\(\int_{\frac{\pi}{3}}^{\frac{2 \pi}{3}} \frac{x}{1+\sin x} d x=\)

2Definite Integration

\(\int_0^2 \frac{3 x+1}{x^2+4} d x=\)

3Definite Integration

The value of the integral $\int_1^2 \frac{x \mathrm{~d} x}{(x+2)(x+3)}$ is

4Definite Integration

\(\int_0^{\frac{\pi}{4}}(\sqrt{\tan x}+\sqrt{\cot x}) d x=\)

5Definite Integration

$\int_2^4 \frac{\log x^2}{\log x^2+\log \left(36-12 x+x^2\right)} \mathrm{d} x$ is equal to

6Definite Integration

The value of $\int_0^2\left[x^2\right] \mathrm{d} x$ is (where $[x]$ denotes the greatest integer function not greater than $x$ )

7Definite Integration

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

8Definite Integration

\(\int_{-1}^3\left(\tan ^{-1}\left(\frac{x}{x^2+1}\right)+\tan ^{-1}\left(\frac{x^2+1}{x}\right)\right) d x=\)

9Definite Integration

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

10Definite Integration

The value of $\int_{-1}^1\left(\sqrt{1+x+x^2}-\sqrt{1-x+x^2}\right) \mathrm{d} x$ is

11Definite Integration

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

12Definite Integration

\(\int_0^{\frac{\pi}{2}} \frac{d x}{1+(\cot x)^{101}}=\)

13Definite Integration

\(\int_1^e \frac{\mathrm{e}^x}{x}(1+x \log x) \mathrm{d} x=\)

14Definite Integration

The value of $\int_1^4 \log [x] \mathrm{d} x$, where $[x]$ is the greatest integer function less than or equal to $x$ is equal to

15Definite Integration

The value of $\int_{\frac{1}{3}}^1 \frac{\left(x-x^3\right)^{\frac{1}{3}}}{x^4} d x$ is

16Definite Integration

The value of $\int_{-3}^3 \sin ^7 x \cos ^{16} x \mathrm{~d} x$ is

17Definite Integration

The value of $\mathrm{I}=\mathrm{I}=\int_{\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{x^2 \cos x}{1+\mathrm{e}^{-x}} \mathrm{~d} x$ is equal to

18Definite Integration

The integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \frac{d x}{\sin 2 x\left(\tan ^5 x+\cot ^5 x\right)}$ is equal to

19Definite Integration

The integral $\int_{\frac{-1}{2}}^{\frac{1}{2}}\left([x]+\log _{\mathrm{e}}\left(\frac{1+x}{1-x}\right)\right) \mathrm{d} x$, where $[x]$ represent greatest integer function, equals

20Definite Integration

The value of $\int_{\frac{\pi}{6}}^{\frac{\pi}{4}} \frac{1}{\sin 2 x\left(\tan ^5 x+\cot ^5 x\right)} d x$ is

21Definite Integration

If $\int_\limits0^{\frac{\pi}{3}} \frac{\tan \theta}{\sqrt{2 k \sec \theta}} d \theta=1-\frac{1}{\sqrt{2}},(k>0)$, then the value of $k$ is

22Definite Integration

The value of the integral $\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\left(x^2+\log \frac{\pi-x}{\pi+x}\right) \cos x d x$ is equal to

23Definite Integration

Let $f$ and $g$ be continuous functions on $[0, a]$ such that $f(x)=f(a-x)$ and $g(x)+g(a-x)=4$, then $\int_0^a f(x) g(x) d x$ is equal to

24Definite Integration

The value of $\mathrm{I}=\int_\limits{\sqrt{\log _{\mathrm{e}}}}^{\sqrt{\log _{\mathrm{e}} 3}} \frac{x \sin x^2}{\sin x^2+\sin \left(\log _{\mathrm{e}} 6-x^2\right)} d x$ is

25Definite Integration

The value of $\int_\limits{-\frac{\pi}{2}}^{\frac{\pi}{2}} \frac{\sin ^2 x}{1+2^x} d x$ is

26Definite Integration

If $[x]$ denotes the greatest integer function, then \(\int_\limits0^5 x^2[x] d x=\)

27Definite Integration

The value of integral $\int_\limits{-2}^0\left(x^3+3 x^2+3 x+5+(x+1) \cos (x+1)\right) d x$ is equal to

28Definite Integration

The value of the integral $\int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}} \mathrm{dx}$ is

29Definite Integration

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

30Definite Integration

\(\int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{\sqrt{1+\cos x}}{(1-\cos x)^{\frac{5}{2}}} d x=\)

31Definite Integration

\(\int_\limits{0.2}^{3.5}[x] \mathrm{d} x=\)

(where $[x]=$ greatest integer not greater than $x$ )

32Definite Integration

If $\mathrm{I}=\int_0^{\frac{\pi}{4}} \log (1+\tan x) \mathrm{d} x$, then value of $\mathrm{I}$ is

33Definite Integration

$\int_\limits0^{\frac{\pi}{2}}|\sin x-\cos x| d x$ has the value

34Definite Integration

$\int_\limits{\frac{-\pi}{4}}^{\frac{\pi}{4}}(\sin x)^{-4} \mathrm{~d} x$ has the value

35Definite Integration

\(\int_\limits0^a \frac{x-a}{x+a} d x=\)

36Definite Integration

\(\int_\limits0^{\frac{\pi}{4}} \log \left(\frac{\sin x+\cos x}{\cos x}\right) d x=\)

37Definite Integration

If \(\mathrm{f}(x)\) is a function satisfying \(\mathrm{f}^{\prime}(x)=\mathrm{f}(x)\) with \(\mathrm{f}(0)=1\) and \(\mathrm{g}(x)\) is a function that satisfies \(\mathrm{f}(x)+\mathrm{g}(x)=x^2\). Then the value of the integral $$\int_\l...

38Definite Integration

\(\int_\limits1^2 \frac{\mathrm{d} x}{\left(x^2-2 x+4\right)^{\frac{3}{2}}}=\frac{\mathrm{k}}{\mathrm{k}+5} \text {, then } \mathrm{k} \text { has the value }\)

39Definite Integration

If \(\mathrm{f}^{\prime}(x)=x-\frac{5}{x^5}\) and \(\mathrm{f}(1)=4\), then \(\mathrm{f}(x)\) is

40Definite Integration

The integral \(\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{3}} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x d x\) is equal to

41Definite Integration

If \(\mathrm{f}^{\prime}(x)=\tan ^{-1}(\sec x+\tan x),-\frac{\pi}{2} < x < \frac{\pi}{2}\) and \(f(0)=0\), then \(\mathrm{f}(1)\) is

42Definite Integration

If \(I_n=\int_\limits0^{\frac{\pi}{4}} \tan ^n \theta d \theta\), then \(I_{12}+I_{10}=\)

43Definite Integration

If $$\mathrm{f}(x)=\left\{\begin{array}{ll}\mathrm{e}^{\cos x} \sin x & , \text { for }|x| \leq 2 \\ 2, & \text { otherwise }\end{array}\right.$$, then \(\int_\limits{-2}^3 \mathrm{f}(x) \mathrm{d} x\) is equal to

44Definite Integration

The integral \(\int_\limits{\pi / 6}^{\pi / 3} \sec ^{\frac{2}{3}} x \operatorname{cosec}^{\frac{4}{3}} x d x\) is equal to

45Definite Integration

\(\int_\limits0^4|2 x-5| d x=\)

46Definite Integration

The value of \(\int_\limits0^\pi\left|\sin x-\frac{2 x}{\pi}\right| \mathrm{d} x\) is

47Definite Integration

\(\int_\limits{-1}^3\left(\cot ^{-1}\left(\frac{x}{x^2+1}\right)+\cot ^{-1}\left(\frac{x^2+1}{x}\right)\right) \mathrm{d} x=\)

48Definite Integration

Let \(\mathrm{f}(x)\) be positive for all real \(x\). If \(\mathrm{I}_1=\int_\limits{1-\mathrm{h}}^{\mathrm{h}} x \mathrm{f}(x(1-x)) \mathrm{d} x\) and \(\mathrm{I}_2=\int_\limits{1-\mathrm{h}}^{\mathrm{h}} \mathrm{f}(x(1-x)) \mathrm{d} x\)...

49Definite Integration

Let \(\mathrm{f}(x)=\int \frac{\sqrt{x}}{(1+x)^2} \mathrm{~d} x, x \geq 0\), then \(\mathrm{f}(3)-\mathrm{f}(1)\) is equal to

50Definite Integration

\(\int\limits_0^\pi \frac{d x}{4+3 \cos x}=\)