Integrals

CBSE Class 12 · Mathematics · 54 past questions

10 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. Q8 2026

   If $\dfrac{d}{dx}(F(x)) = \dfrac{1}{e^x + 1}$, then find $F(x)$ given that $F(0) = \log \dfrac{1}{2}$.

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3. Q9 2026

   $\int \frac{dx}{2^x + 2^{-x}}$ is equal to…

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4. 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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5. Q25 2024

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

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6. Q34 2024

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

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7. Q37 2023

   $\int 2^{x+2}\,dx$ is equal to…

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8. Q42 2023

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

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9. Q47 2023

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

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10. Q52 2022

    If $\frac{d}{dx}[F(x)]=\frac{\sec^4 x}{\operatorname{cosec}^4 x}$ and…

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