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Definite Integration

MHT-CET Maths. Try each one first, then open its answer.

Top 10 MHT-CET PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 13 times: May 2021 S1, 3 May 2023 S2, 4 May 2023 S1, 15 May 2023 S1, 10 May 2024 S2, 19 Apr 2025 S2, 20 Apr 2025 S1, 25 Apr 2025 S2, 13 Apr 2026 S1, 15 Apr 2026 S2, 16 Apr 2026 S2, 20 Apr 2026 S2, 19 May 2026 S1. This one: 19 May 2026 S1 See all 13 of this type

    83
    Let f(x)f(x) be odd and continuous on [−a,a][-a, a]. Then the value of ∫−aaxf(x2)dx\int_{-a}^{a} xf(x^2)dx is:

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  2. Question 2

    This type asked 9 times: 10 May 2023 S1, 12 May 2024 S1, 12 May 2024 S2, 20 Apr 2025 S1, 26 Apr 2025 S2, 15 Apr 2026 S2, 18 Apr 2026 S2, 19 Apr 2026 S2, 20 Apr 2026 S2. This one: 20 Apr 2026 S2 See all 9 of this type

    82
    The value of the integral ∫1/ee∣log⁡x∣x2 dx\int_{1/e}^{e}\dfrac{|\log x|}{x^2}\,dx is

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  3. Question 3

    This type asked 8 times: 2 May 2023 S2, 15 May 2023 S2, 20 Apr 2025 S2, 21 Apr 2025 S1, 23 Apr 2025 S1, 25 Apr 2025 S1, 26 Apr 2025 S2, 15 May 2026 S2. This one: 15 May 2026 S2 See all 8 of this type

    82
    ∫π/53π/1011+tan⁡x dx=⋯\displaystyle\int_{\pi/5}^{3\pi/10}\dfrac{1}{1 + \sqrt{\tan x}}\, dx = \cdots

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  4. Question 4

    This type asked 8 times: May 2022 S1, 11 May 2023 S1, 19 Apr 2025 S1, 21 Apr 2025 S1, 17 Apr 2026 S2, 18 Apr 2026 S1, 19 Apr 2026 S1, 12 May 2026 S2. This one: 12 May 2026 S2 See all 8 of this type

    83
    If f(x)={[x]⋅∣x∣x,x≠00,x=0f(x) = \begin{cases} \dfrac{[x] \cdot |x|}{x}, & x \neq 0 \\ 0, & x = 0 \end{cases}, where [x][x] and ∣x∣|x| denote the greatest integer function and the modulus function respectively, then ∫−21f(x) dx=…\int_{-2}^{1} f(x)\,dx = \ldots

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  5. Question 5

    This type asked 5 times: 9 May 2023 S1, 16 May 2023 S1, 15 Apr 2026 S1, 17 Apr 2026 S1, 12 May 2026 S2. This one: 12 May 2026 S2 See all 5 of this type

    82
    The value of the integral ∫−111(1+ex)(1+x2) dx\int_{-1}^{1}\dfrac{1}{(1 + e^x)(1 + x^2)}\,dx is....

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  6. Question 6

    This type asked 4 times: 10 May 2023 S2, 11 May 2023 S2, 14 May 2026 S2, 19 May 2026 S2. This one: 19 May 2026 S2 See all 4 of this type

    81
    If ∫0πlog⁡(sin⁡x) dx=k\int_0^\pi \log(\sin x)\,dx = k, then the value of ∫0π4log⁡(1+tan⁡x) dx\int_0^{\frac{\pi}{4}}\log(1 + \tan x)\,dx in terms of kk is...

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  7. Question 7

    This type asked 4 times: 16 May 2023 S2, 11 Apr 2026 S1, 20 Apr 2026 S1, 13 May 2026 S1. This one: 13 May 2026 S1 See all 4 of this type

    81
    Let In=∫nn+1x[x] dxI_n = \int_n^{n+1}x[x]\,dx, where [x][x] denotes greatest integer function and n∈Nn \in N. If In=18I_n = 18, then the value of nn is...

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  8. Question 8

    This type asked 4 times: 14 May 2024 S2, 17 Apr 2026 S1, 20 Apr 2026 S2, 12 May 2026 S1. This one: 12 May 2026 S1 See all 4 of this type

    82
    If nn is an odd natural number and In=∫01ex(x−1)n dxI_n = \int_0^1 e^x(x - 1)^n\,dx, then the value of In+nIn−1I_n + nI_{n-1} is equal to ...

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  9. Question 9

    This type asked 4 times: 11 Apr 2026 S1, 11 Apr 2026 S2, 13 Apr 2026 S1, 13 Apr 2026 S2. This one: 13 Apr 2026 S2 See all 4 of this type

    81
    If ∫0a(x2−4x+1) dx=6\int_0^a(x^2 - 4x + 1)\,dx = 6, then the real value of aa is

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  10. Question 10

    Asked 3 times: 10 May 2023 S2, 11 May 2023 S2, 14 May 2026 S2 See all 3 times it was asked

    84
    ∫0π/4log⁡(1+tan⁡x) dx=…\displaystyle\int_0^{\pi/4}\log(1 + \tan x)\,dx = \ldots

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