Integrals

CBSE Class 12 · Mathematics · 54 past questions

13 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. Q3 2026

   Evaluate : $\displaystyle\int_0^1 x\tan^{-1}x\,dx$.

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4. Q4 2026

   Find $\displaystyle\int\sqrt{\dfrac{x+2}{x-2}}\,dx$

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5. 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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6. Q6 2026

   Find : $\displaystyle\int \dfrac{x + 2}{\sqrt{9x - x^2}}\, dx$

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7. Q7 2026

   (a) Evaluate : $\displaystyle\int_{\pi/12}^{5\pi/12} \dfrac{dx}{1 + \sqrt{\cot x}}$

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8. 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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9. Q9 2026

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

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10. Q10 2026

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

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11. Q11 2026

    Find…

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12. Q12 2026

    Evaluate: $\int_0^{\pi} \frac{\sin^{2026}x}{\sin^{2026}x + \cos^{2026}x}\,dx$

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13. Q13 2026

    Find: $\int \frac{\cos x}{(2+\sin x)(4+\sin x)}\,dx$

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