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Integrals

Bihar Board Class 12 · Mathematics · 212 past questions

68 of 212 · show all

  1. Q3 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int \cos\sqrt{x}\,dx =$
  2. Q5 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int \frac{\tan(\sin^{-1}x)}{\sqrt{1-x^2}}\,dx =$
  3. Q7 2026 Set A2026 Set H2026 Set E2026 Set F2026 Set J2026 Set B
    $\int_0^1 \frac{x^3\,dx}{1+x^8} =$
  4. Q8 2026 Set A
    $\int_0^{1} x e^{x} \, dx =$
  5. Q16 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2024 Set J2024 Set D
    $\int_0^{a} \frac{\sqrt{x}}{\sqrt{a-x}+\sqrt{x}}\,dx =$
  6. Q19 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_0^1 \frac{e^{\sqrt{x}}}{\sqrt{x}}\,dx =$
  7. Q21 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I
    $\int \frac{\cos 2x}{(\sin x + \cos x)^2}\,dx =$
  8. Q22 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_0^{\pi/3} \cos^3 x\, dx =$
  9. Q23 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_0^{\pi/2} \frac{\sin x}{\sin x+\cos x}\, dx =$
  10. Q25 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    Integrate : $\int \sec^4 x\,dx$.
  11. Q26 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int \frac{dx}{e^{x}+e^{-x}} =$
  12. Q29 2026 Set C
    $\int_0^1 x e^{x}\,dx =$
  13. Q30 2026 Set C2026 Set D
    $\displaystyle\int_0^1 \frac{x^3\,dx}{1+x^8}=$
  14. Q35 2026 Set E
    Solve: $\int_1^2\frac{\log x}{x}dx$.
  15. Q36 2026 Set H2026 Set E2026 Set F2026 Set D2026 Set J2026 Set B2025 Set A20252025 Set E2021 Set I
    $\int_0^1 x e^x\,dx =$
  16. Q39 2025
    $\int \dfrac{dx}{\sin^2 x \cos^2 x} =$
  17. Q45 2025
    $\int 2\left(\sin^{-1}(\cos x)\right)dx =$
  18. Q46 2025
    $\int e^x\left(\dfrac{1}{\sqrt{1-x^2}} + \sin^{-1}x\right)dx =$
  19. Q47 2025
    $\int 4x\log x\,dx =$
  20. Q50 2025
    $\int \dfrac{4x+1}{\sqrt{2x^2+x-3}}\,dx =$
  21. Q51 2025
    $\int e^x[2\cos 2x+\sin 2x]\,dx =$
  22. Q57 2025
    $\int_{-\pi/2}^{\pi/2} (x^5 + x\cos x + \sin^7 x + 1)\,dx =$
  23. Q58 2025
    $\displaystyle\int \left(\dfrac{x^3-x^2+x-1}{x^2+1}\right) dx =$
  24. Q61 2025
    Integrate: $\int \frac{x^2+2}{x+1}\,dx$
  25. Q63 2025
    If $\int_0^a \frac{1}{1+4x^2}\,dx = \frac{\pi}{8}$ then find the value of $a$.
  26. Q64 2025
    Integrate: $\int \frac{\sin x}{3+4\cos^2 x}\,dx$
  27. Q65 2025
    Integrate: $\int \frac{\sin^6 x+\cos^6 x}{\sin^2 x\cos^2 x}\,dx$
  28. Q67 2025
    Integrate: $\int_{-\pi/4}^{\pi/4} \sin^2 x\, dx$
  29. Q69 20252025 Set A2025 Set E
    $\int_0^{\pi/2} \frac{\sqrt{\cos x}}{\sqrt{\sin x}+\sqrt{\cos x}}\,dx =$
  30. Q72 2025 Set A2025 Set E
    $\int \dfrac{(\sqrt{x}+1)^2}{x\sqrt{x}+2x+\sqrt{x}}\,dx =$
  31. Q76 2025 Set A2025 Set E
    $\int \frac{\cos 2x}{\cos x+\sin x}\,dx =$
  32. Q79 2025 Set A
    $\int \log x^2\,dx =$
  33. Q80 2025 Set A
    $\int (\sin 3x+4\sin^3 x)\,dx =$
  34. Q82 2025 Set A2025 Set E
    $\int_{0}^{1}\frac{4\tan^{-1}x}{1+x^2}\,dx =$
  35. Q84 2025 Set A2025 Set E
    $\int_0^a \frac{x\,dx}{2\sqrt{a^2-x^2}} =$
  36. Q86 2025 Set A2025 Set E
    $\int_0^{\pi/2} \log\tan x\,dx =$
  37. Q98 2025 Set E
    $\int \log x^{2}\,dx =$
  38. Q99 2025 Set E
    $\int (\sin 3x + 4\sin^{3}x)\,dx =$
  39. Q112 2024 Set D2024 Set J
    $\int_0^{\pi/6}\cos x\cdot\cos 2x\,dx =$
  40. Q114 2024 Set D
    $\int\frac{\cos2x}{\cos^2x\cdot\sin^2x}dx=$
  41. Q116 2024 Set D2024 Set J
    $\int \frac{x^3\,dx}{1+x^8} =$
  42. Q118 2024 Set D2024 Set J
    $\int \sqrt{1-\sin 2x}\, dx =$
  43. Q120 2024 Set D2024 Set J
    $\int\frac{\cos\sqrt{x}}{\sqrt{x}}\,dx =$
  44. Q125 2024 Set D2024 Set J
    $\int \sec^5 x\tan x\,dx=$
  45. Q129 2024 Set J2024 Set D2021 Set J
    $\int \frac{x^4-1}{x^2+1}\,dx =$
  46. Q130 2024 Set J
    $\int \frac{\cos 2x}{\cos^2 x\cdot\sin^2 x}\,dx=$
  47. Q134 2023
    $\int (\cos\theta \, \text{cosec}^2\theta - \cos\theta \, \cot^2\theta) \, d\theta =$
  48. Q136 2023
    $\int \frac{3\cos x - 2\sin x}{2\cos x + 3\sin x} \, dx =$
  49. Q139 20232023 Set E
    $\int_{-1}^{1} \log\left(\frac{3+x}{3-x}\right) \, dx =$
  50. Q146 20232023 Set E
    $\int e^x (x^3+3x^2)\,dx =$
  51. Q150 2023
    $\int_{-1}^{1} x^{17} \, x \, dx =$
  52. Q156 20232023 Set E
    $\int \frac{dx}{1+36x^2} =$
  53. Q163 2023 Set E
    $\int(\cos\theta\operatorname{cosec}^2\theta-\cos\theta\cot^2\theta)\,d\theta=$
  54. Q165 2023 Set E
    $\int\dfrac{3\cos x-2\sin x}{2\cos x+3\sin x}\,dx=$
  55. Q166 2023 Set E
    Find the value of $\int_1^2\left(\frac1x-\frac1{2x^2}\right)e^{2x}\,dx$.
  56. Q170 2021 Set J2021 Set I
    $\int_0^{\pi/2} \log\cot\theta\,d\theta =$
  57. Q171 2021 Set J2021 Set I
    $\int_0^{\pi/2} \frac{\cos\theta}{\cos\theta+\sin\theta}\,d\theta =$
  58. Q172 2021 Set J2021 Set I
    $\int \dfrac{\sec x}{\sec x+\tan x}\,dx =$
  59. Q185 2019 Set F
    $\int_0^{\pi/2} \sin^3 x \cos x\,dx = ?$
  60. Q188 2018
    $\int\dfrac{xe^{x}}{(x+1)^{2}}\,dx=$
  61. Q192 20182015
    $\int \dfrac{dx}{x+\sqrt{x}}$
  62. Q193 2018
    Integrate $\int \sec^n\theta \cdot \tan\theta \, d\theta$
  63. Q194 2018
    Prove that $\int_0^{2\pi} |\cos x|\,dx = 4$
  64. Q199 2017
    Integrate $\int \sin^2 x \cdot \cos^2 x \, dx$
  65. Q200 2017
    Evaluate $\int_0^a \frac{x\,dx}{\sqrt{a^2 - x^2}}$
  66. Q201 20162015
    Integrate $\int e^x \cos x\,dx$
  67. Q204 2016
    $\int\frac{dx}{1-\sin x}=$
  68. Q212 2015
    Evaluate $\int_0^{\pi/4} \sin^2 x\,dx$