Definite Integration

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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

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Mathematics / Calculus

2019-2026

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108

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2022-2026

146

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2017-2026

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108 in last 5 years146 in last 10 years

Definite Integration Questions

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1Definite Integration

If $\int_0^1 \dfrac{dx}{\sqrt{x + 1} - \sqrt{x}} = \sqrt{2}k$, then the value of $k$ is...

2Definite Integration

If $[x]$ denotes the greatest integer less than or equal to $x$, then the value of the integral $\int_0^2 x^2[x]\, dx$ is equal to

3Definite Integration

If $I_n = \int\limits_0^{\pi/4}\tan^n x\ dx, n \in N$ then $I_{n+2} + I_n$ is equal to

4Definite Integration

If $\int\limits_{-\pi/2}^{\pi/2}(\sin^2 x + \sin^3 x)dx = k$, then the value of $k$

5Definite Integration

The value of the integral $\int\limits_{1/e}^{e}\dfrac{|\log x|}{x^2}dx$ is

6Definite Integration

The value of $\displaystyle\int_2^4 (\{x\} + [x])\,dx =$...(where $\{x\}$ and $[x]$ are the fractional part function and the greatest integer function, respectively)

7Definite Integration

If $[x]$ is the greatest integer function not greater than $x$, then the value of $\displaystyle\int_0^2 x[x^2]\,dx$ is...

8Definite Integration

If $f(x)$ is an antiderivative of $\dfrac{x + 1}{\sqrt{x - 1}}$ with respect to $x$, then value of $f(5) - f(2)$ is...

9Definite Integration

The value of integral $\int_0^\infty \dfrac{1}{1 + e^x}\,dx$ is...

10Definite Integration

If $f(x) = |5x - 3|$ is defined on interval $[0, 1]$, then the value of $\int_0^1 f(x)\,dx$ is...

11Definite Integration

If $[\cdot]$ denotes the greatest integer function, then $\int_0^{\pi/3}[\tan x]\,dx = $

12Definite Integration

The value of the definite integral $\int_0^{\log_e 5}\dfrac{e^x\sqrt{e^x-1}}{e^x+3}\,dx$ is equal to...

13Definite Integration

$\int_0^2 |4x - 5|\,dx = \ldots$

14Definite Integration

If $\int_0^2 x(2 - x)^b\,dx = \dfrac{32}{7}$, where $b \in N$ then $b = $

15Definite Integration

If $I_n = \int_1^e (\log_e x)^n\,dx$ where $n \in Z^+$ and $I_m + mI_{2026} = e$, then $m = $

16Definite Integration

The value of $\int_0^\pi \dfrac{1}{1 + 2^{\cos x}}\,dx$ is _____

17Definite Integration

Let $f(x) = x - [x]$ for every real number $x$, where $[x]$ is integral part of $x$. then $\int\limits_{-1}^{1} f(x)\, dx$ is

18Definite Integration

The value of the definite integral $\int_0^{\pi}\dfrac{1}{5 + 4\cos x}\, dx$ is equal to ...

19Definite Integration

If $\int_a^b(x^2 - x)\, dx = 18, \int_a^b x^3\, dx = 0$, then $a + b$ is equal to

20Definite Integration

The function $f(x) = \int_0^x\dfrac{dt}{1 + \cos t}$ satisfies which of the following differential equations?

21Definite Integration

$\displaystyle\int_0^{\log 5} \dfrac{e^x\sqrt{e^x - 1}}{e^x + 3}\,dx =$

22Definite Integration

$\displaystyle\int_{\pi/6}^{\pi/3} \dfrac{\sin x - \cos x}{1 + \sin x\cos x}\,dx =$

23Definite Integration

The value of $\int_{-\pi}^{\pi}\dfrac{2x(1 + \sin x)}{1 + \cos^2 x}dx$ is...

24Definite Integration

The value of integral $\int_0^1\cot^{-1}(1 + x^2 - x)\,dx$ is...

25Definite Integration

The value of the integral $\int_{-\pi/2}^{\pi/2}\left(\dfrac{x^2 \cos x}{1+e^x}\right)dx$ is equal to $\left(\dfrac{\pi^2}{A}\right) - B$. Then $\left(\dfrac{A}{B}\right) = $

26Definite Integration

$\int_0^{\log 10}\left[\dfrac{e^x \sqrt{e^x - 1}}{e^x + 8}\right]dx = $

27Definite Integration

If $f(x)$ is an even function, then $\int\limits_{-2}^{2} (|x| + f(x)\sin x)\, \text{d}x$ is

28Definite Integration

$\int\limits_{0}^{\pi} |\sin 2x|\, \text{d}x =$

29Definite Integration

The value of the integral $\displaystyle\int_{-\sqrt{3}}^{\sqrt{3}} \dfrac{(2x^9 + 3x^8 - 5x^7 + 9x^6 + 4x^3 - x + 3)}{x^2 + 3} \, dx$ is

30Definite Integration

If $\displaystyle\int_0^a \dfrac{dx}{1 + 4x^2} = \dfrac{\pi}{8}$, then $a =$

31Definite Integration

If $\int_{\pi/6}^{\pi/3} \dfrac{1}{1+\sin x + \cos x}dx = \log 2$, then the value of $\int_{\pi/6}^{\pi/3} \dfrac{\cos x}{1+\sin x + \cos x}dx = $ ............

32Definite Integration

If $\int_0^a (x^2 - 4x + 1)dx = 6$, then the real value of $a$ is

33Definite Integration

If $\int_1^a (2x + 1) dx = 5$, then the sum of the values of $a$ is..

34Definite Integration

If $[\cdot]$ denotes the greatest integer function, then $\int_1^4 x[x] dx$ is equal to

35Definite Integration

If $\int_{0}^{k} \dfrac{1}{1 + 4^x} dx = \log_2\left(\dfrac{4}{3}\right)$, then $k = $ _____

36Definite Integration

If $\int_{2}^{e}\left[\dfrac{1}{\log x} - \dfrac{1}{(\log x)^2}\right] dx = a + \dfrac{b}{\log 2}$, then values of $a$ and $b$ are

37Definite Integration

The value of $\int_0^\pi\left|\sin ^3 x\right| \mathrm{d} x$ is

38Definite Integration

\(\int_0^1 \log (x+1) d x=\)

39Definite Integration

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

40Definite Integration

$\int_{\frac{1}{2}}^2 \frac{1}{x} \operatorname{cosec}^{101}\left(x-\frac{1}{x}\right) \mathrm{d} x=$

41Definite Integration

\(\int_0^{\frac{\pi}{2}} \frac{300 \sin x+100 \cos x}{\sin x+\cos x} d x=\ldots\)

42Definite Integration

\(\int\limits_0^1 x\left|x-\frac{1}{2}\right| \mathrm{d} x=\)

43Definite Integration

\(\int\limits_0^1 \frac{1}{2+\sqrt{x}} d x=\)

44Definite Integration

\(\int_1^3 \frac{\log x^2}{\log \left(16 x^2-8 x^3+x^4\right)} d x=\)

45Definite Integration

\(\int_{\log \frac{1}{2}}^{\log 2} \sin \left(\frac{\mathrm{e}^x-1}{\mathrm{e}^x+1}\right) \mathrm{d} x=\)

46Definite Integration

\(\int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} \sin ^{-4} x d x=\)

47Definite Integration

\(\int_3^5 \frac{\sqrt{x} \mathrm{~d} x}{\sqrt{8-x}+\sqrt{x}}=\)

48Definite Integration

The value of $\int_0^1 \tan ^{-1}\left(1-x+x^2\right) \mathrm{d} x$ is

49Definite Integration

\(\int_0^1 \log \left(\frac{1}{x}-1\right) d x=\)

50Definite Integration

\(\int\limits_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\left(x^2+\log \left(\frac{\pi-x}{\pi+x}\right) \cdot \cos x\right) d x=\)

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