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Integrals

Bihar Board Class 12 · Mathematics · 212 past questions

38 of 212 · show all

  1. Q1 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I
    $\int (x+2)\,dx =$
  2. Q2 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I
    $\int \frac{dx}{x-1} =$
  3. Q3 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int \cos\sqrt{x}\,dx =$
  4. Q4 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int \sin^2\frac{x}{2}\,dx =$
  5. Q5 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int \frac{\tan(\sin^{-1}x)}{\sqrt{1-x^2}}\,dx =$
  6. Q6 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B20252019 Set F
    $\int_0^1 \frac{dx}{1+x^2} =$
  7. Q7 2026 Set A2026 Set H2026 Set E2026 Set F2026 Set J2026 Set B
    $\int_0^1 \frac{x^3\,dx}{1+x^8} =$
  8. Q8 2026 Set A
    $\int_0^{1} x e^{x} \, dx =$
  9. Q9 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_{-2}^{2} |x|\,dx =$
  10. Q10 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2024 Set J2024 Set D2021 Set J2021 Set I
    $\int \frac{1-\cos 2x}{1+\cos 2x}\,dx =$
  11. Q11 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int e^x\left(\tan^{-1}x + \frac{1}{1+x^2}\right)dx =$
  12. Q12 2026 Set A2026 Set H2026 Set E2026 Set F2026 Set J2026 Set B
    $\int_1^e \frac{(\log x)^2}{x}\,dx =$
  13. Q13 2026 Set A2026 Set H2026 Set E2026 Set F2026 Set J2026 Set B
    $\int_0^{\pi/4} \frac{e^{\tan x}}{\cos^2 x}\,dx =$
  14. Q14 2026 Set A2026 Set H2026 Set E2026 Set F2026 Set J2026 Set B2024 Set J2024 Set D2021 Set J2021 Set I2019 Set F
    $\int_0^{\pi/2} \cos^2 x\,dx =$
  15. Q15 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_0^{2\pi} |\sin x|\,dx =$
  16. Q16 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2024 Set J2024 Set D
    $\int_0^{a} \frac{\sqrt{x}}{\sqrt{a-x}+\sqrt{x}}\,dx =$
  17. Q17 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2016
    $\int \frac{dx}{x^2+a^2} =$
  18. Q18 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I
    $\int \log x\, dx =$
  19. Q19 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_0^1 \frac{e^{\sqrt{x}}}{\sqrt{x}}\,dx =$
  20. Q20 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_1^4 \frac{dx}{\sqrt{x}} =$
  21. Q21 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I
    $\int \frac{\cos 2x}{(\sin x + \cos x)^2}\,dx =$
  22. Q22 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_0^{\pi/3} \cos^3 x\, dx =$
  23. Q23 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_0^{\pi/2} \frac{\sin x}{\sin x+\cos x}\, dx =$
  24. Q24 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set B
    $\int_{-\pi}^{\pi} \sin^5 x\, dx =$
  25. Q25 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    Integrate : $\int \sec^4 x\,dx$.
  26. Q26 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int \frac{dx}{e^{x}+e^{-x}} =$
  27. Q27 2026 Set A2026 Set H2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    Solve : $\int_1^2 \frac{\log x}{x}\,dx$.
  28. Q28 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_0^a \sqrt{a^2 - x^2}\,dx =$
  29. Q29 2026 Set C
    $\int_0^1 x e^{x}\,dx =$
  30. Q30 2026 Set C2026 Set D
    $\displaystyle\int_0^1 \frac{x^3\,dx}{1+x^8}=$
  31. Q31 2026 Set C2026 Set D
    $\displaystyle\int_1^e \frac{(\log x)^2}{x}\,dx=$
  32. Q32 2026 Set C2026 Set D
    $\displaystyle\int_0^{\pi/4} \frac{e^{\tan x}}{\cos^2 x}\,dx=$
  33. Q33 2026 Set C
    $\displaystyle\int_{0}^{\pi/2} \cos^2 x\,dx$
  34. Q34 2026 Set D
    $\cos^2 x\,dx$ integrated from $0$ to $\pi/2$: $\int_0^{\pi/2} \cos^2 x\, dx =$
  35. Q35 2026 Set E
    Solve: $\int_1^2\frac{\log x}{x}dx$.
  36. Q36 2026 Set H2026 Set E2026 Set F2026 Set D2026 Set J2026 Set B2025 Set A20252025 Set E2021 Set I
    $\int_0^1 x e^x\,dx =$
  37. Q37 2026 Set J2026 Set C2026 Set B2026 Set H
    Prove that $\int_0^{\pi/2} (\sqrt{\tan x} + \sqrt{\cot x})\, dx = \pi\sqrt{2}$.
  38. Q38 2026 Set J
    $\int_{-\pi}^{\pi} \sin^3 x \, dx =$