Integrals

CBSE Class 12 · Mathematics · 54 past questions

15 of 54 · show all

1. Q1 2026

   If $\int \frac{3ax}{b^2 + c^2x^2}\,dx = A \log \left| b^2 + c^2x^2 \right| + K$, then the value of A is

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2. Q2 2026

   The value of $\int_{-1}^{1} \frac{x^3}{x^2 + 2|x| + 1}\,dx$ is

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3. Q5 2026

   If $\int_0^{2a} \frac{1}{1+4x^2}\,dx = \frac{\pi}{6}$, then the value of a is

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4. Q10 2026

   $\int_{-1}^{1}(1-|x|)\,dx$ is equal to…

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5. Q14 2025

   $\int_{-1}^{1} \frac{|x|}{x}\, dx$, $x \neq 0$ is equal to

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6. Q15 2025

   If $\int \frac{2^{\frac{1}{x}}}{x^2}\,dx = k \cdot 2^{\frac{1}{x}} + C$, then k is equal to

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7. Q17 2025

   If $f(2a - x) = f(x)$, then $\displaystyle\int_0^{2a} f(x)\,dx$ is

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8. Q25 2024

   $\displaystyle\int_a^b f(x)\,dx$ is equal to…

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9. Q26 2024

   Find : $\int x\sqrt{1 + 2x}\,dx$

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10. Q29 2024

    $\int_{-a}^{a} f(x)\,dx = 0$, if…

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11. Q34 2024

    Find : $\displaystyle\int \dfrac{e^{4x} - 1}{e^{4x} + 1}\,dx$

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12. Q37 2023

    $\int 2^{x+2}\,dx$ is equal to…

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13. Q42 2023

    If $\frac{d}{dx}(f(x)) = \log x$, then $f(x)$ equals…

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14. Q43 2023

    $\int_0^{\pi/6} \sec^2\left(x - \frac{\pi}{6}\right) dx$ is equal to…

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15. Q47 2023

    If $\frac{d}{dx}[f(x)] = ax + b$ and $f(0) = 0$, then $f(x)$ is equal to

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