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← CBSE Class 12 PYQ

Integrals

CBSE Class 12 · Mathematics · 54 past questions

  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
  2. Q2 2026
    The value of $\int_{-1}^{1} \frac{x^3}{x^2 + 2|x| + 1}\,dx$ is
  3. Q3 2026
    Evaluate : $\displaystyle\int_0^1 x\tan^{-1}x\,dx$.
  4. Q4 2026
    Find $\displaystyle\int\sqrt{\dfrac{x+2}{x-2}}\,dx$
  5. Q5 2026
    If $\int_0^{2a} \frac{1}{1+4x^2}\,dx = \frac{\pi}{6}$, then the value of a is
  6. Q6 2026
    Find : $\displaystyle\int \dfrac{x + 2}{\sqrt{9x - x^2}}\, dx$
  7. Q7 2026
    (a) Evaluate : $\displaystyle\int_{\pi/12}^{5\pi/12} \dfrac{dx}{1 + \sqrt{\cot x}}$
  8. Q8 2026
    If $\dfrac{d}{dx}(F(x)) = \dfrac{1}{e^x + 1}$, then find $F(x)$ given that $F(0) = \log \dfrac{1}{2}$.
  9. Q9 2026
    $\int \frac{dx}{2^x + 2^{-x}}$ is equal to…
  10. Q10 2026
    $\int_{-1}^{1}(1-|x|)\,dx$ is equal to…
  11. Q11 2026
    Find…
  12. Q12 2026
    Evaluate: $\int_0^{\pi} \frac{\sin^{2026}x}{\sin^{2026}x + \cos^{2026}x}\,dx$
  13. Q13 2026
    Find: $\int \frac{\cos x}{(2+\sin x)(4+\sin x)}\,dx$
  14. Q14 2025
    $\int_{-1}^{1} \frac{|x|}{x}\, dx$, $x \neq 0$ is equal to
  15. Q15 2025
    If $\int \frac{2^{\frac{1}{x}}}{x^2}\,dx = k \cdot 2^{\frac{1}{x}} + C$, then k is equal to
  16. Q16 2025
    Find : $\int \frac{x+\sin x}{1+\cos x}\,dx$
  17. Q17 2025
    If $f(2a - x) = f(x)$, then $\displaystyle\int_0^{2a} f(x)\,dx$ is
  18. Q18 2025
    Evaluate : $\int_0^{\pi/4} \sqrt{1+\sin 2x}\,dx$
  19. Q19 2025
    Find : $\int \frac{1}{x}\sqrt{\frac{x+a}{x-a}}\,dx$.
  20. Q20 2025
    Find : $\int \frac{x^2+x+1}{(x+2)(x^2+1)}\,dx$.
  21. Q21 2025
    $\int \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha}\,dx$ is equal to…
  22. Q22 2025
    The value of $\int_0^1 \frac{dx}{e^x + e^{-x}}$ is…
  23. Q23 2025
    Evaluate…
  24. Q24 2025
    Find…
  25. Q25 2024
    $\displaystyle\int_a^b f(x)\,dx$ is equal to…
  26. Q26 2024
    Find : $\int x\sqrt{1 + 2x}\,dx$
  27. Q27 2024
    Find…
  28. Q28 2024
    Evaluate…
  29. Q29 2024
    $\int_{-a}^{a} f(x)\,dx = 0$, if…
  30. Q30 2024
    Evaluate…
  31. Q31 2024
    Find : $\int \frac{x^2+1}{(x^2+2)(x^2+4)}\,dx$
  32. Q32 2024
    Find : $\int \frac{2+\sin 2x}{1+\cos 2x}\,e^x\,dx$
  33. Q33 2024
    $\int_0^{\pi/2} \frac{\sin x-\cos x}{1+\sin x\cos x}\,dx$ is equal to…
  34. Q34 2024
    Find : $\displaystyle\int \dfrac{e^{4x} - 1}{e^{4x} + 1}\,dx$
  35. Q35 2024
    Evaluate : $\int_{-2}^{2}\sqrt{\frac{2-x}{2+x}}\,dx$
  36. Q36 2024
    Find : $\int x^2 \cdot \sin^{-1}(x^{3/2})\,dx$
  37. Q37 2023
    $\int 2^{x+2}\,dx$ is equal to…
  38. Q38 2023
    $\int \frac{2\cos 2x - 1}{1 + 2\sin x}\,dx$ is equal to…
  39. Q39 2023
    Evaluate…
  40. Q40 2023
    Evaluate…
  41. Q41 2023
    Find…
  42. Q42 2023
    If $\frac{d}{dx}(f(x)) = \log x$, then $f(x)$ equals…
  43. Q43 2023
    $\int_0^{\pi/6} \sec^2\left(x - \frac{\pi}{6}\right) dx$ is equal to…
  44. Q44 2023
    Evaluate : $\int_0^{\pi/2} [\log(\sin x) - \log(2\cos x)]\,dx$.
  45. Q45 2023
    Find…
  46. Q46 2023
    Evaluate : $\int_0^{\pi/2} e^x \sin x\,dx$
  47. Q47 2023
    If $\frac{d}{dx}[f(x)] = ax + b$ and $f(0) = 0$, then $f(x)$ is equal to
  48. Q48 2023
    Anti-derivative of $\frac{\tan x - 1}{\tan x + 1}$ with respect to $x$ is
  49. Q49 2023
    Evaluate $\int_0^{\pi/4} \log(1 + \tan x)\, dx$.
  50. Q50 2023
    Find $\int e^{\cot^{-1}x}\left(\frac{1-x+x^2}{1+x^2}\right)dx$.
  51. Q51 2023
    Evaluate $\int_{\log\sqrt{2}}^{\log\sqrt{3}} \frac{1}{(e^x+e^{-x})(e^x-e^{-x})}\,dx$
  52. Q52 2022
    If $\frac{d}{dx}[F(x)]=\frac{\sec^4 x}{\operatorname{cosec}^4 x}$ and…
  53. Q53 2022
    Find : $\int\frac{dx}{\sqrt{x}+\sqrt[3]{x}}$.
  54. Q54 2022
    Evaluate : $\int_0^{\pi} \frac{x}{1+\sin x}\,dx$.