Integrals

Bihar Board Class 12 · Mathematics · 212 past questions

69 of 212 · show all

1. Q6 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B20252019 Set F

   $\int_0^1 \frac{dx}{1+x^2} =$

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2. Q36 2026 Set H2026 Set E2026 Set F2026 Set D2026 Set J2026 Set B2025 Set A20252025 Set E2021 Set I

   $\int_0^1 x e^x\,dx =$

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3. Q39 2025

   $\int \dfrac{dx}{\sin^2 x \cos^2 x} =$

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4. Q40 2025

   $\int \dfrac{dx}{\sqrt{a^2-x^2}} =$

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5. Q41 2025

   $\int x^2\left(\dfrac{1}{x^2}+1\right)dx =$

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6. Q42 2025

   $\int \dfrac{5-3\sin x}{\cos^2 x}\,dx =$

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7. Q43 2025

   $\int \text{cosec}\,x\,dx =$

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8. Q44 2025

   $\int \dfrac{(7+\log x)^2}{x}\,dx$

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9. Q45 2025

   $\int 2\left(\sin^{-1}(\cos x)\right)dx =$

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10. Q46 2025

    $\int e^x\left(\dfrac{1}{\sqrt{1-x^2}} + \sin^{-1}x\right)dx =$

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11. Q47 2025

    $\int 4x\log x\,dx =$

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12. Q48 2025

    $\displaystyle\int \frac{\cos\sqrt{x}}{\sqrt{x}}\,dx =$

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13. Q49 2025

    $\int \dfrac{3x^2}{x^6+1}\,dx =$

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14. Q50 2025

    $\int \dfrac{4x+1}{\sqrt{2x^2+x-3}}\,dx =$

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15. Q51 2025

    $\int e^x[2\cos 2x+\sin 2x]\,dx =$

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16. Q52 2025

    $\int \dfrac{dx}{\sqrt{x^2+a^2}} =$

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17. Q53 2025

    $\int_{-1}^{1} \sin^7 x \cos^6 x\,dx =$

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18. Q54 2025

    $\int_0^{\pi/4} \tan x\,dx =$

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19. Q55 2025

    $\int_2^3 \frac{1}{x}\,dx =$

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20. Q56 2025

    $\int \frac{\sin^{-1}x}{\sqrt{1-x^2}}\,dx$

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21. Q57 2025

    $\int_{-\pi/2}^{\pi/2} (x^5 + x\cos x + \sin^7 x + 1)\,dx =$

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22. Q58 2025

    $\displaystyle\int \left(\dfrac{x^3-x^2+x-1}{x^2+1}\right) dx =$

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23. Q59 2025

    $\displaystyle\int e^{-7x}\, dx =$

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24. Q60 2025

    $\displaystyle\int (5x^4+2x+\sin x)\, dx =$

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25. Q61 2025

    Integrate: $\int \frac{x^2+2}{x+1}\,dx$

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26. Q62 2025

    Integrate: $\int \frac{dx}{1+\cos x}$

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27. Q63 2025

    If $\int_0^a \frac{1}{1+4x^2}\,dx = \frac{\pi}{8}$ then find the value of $a$.

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28. Q64 2025

    Integrate: $\int \frac{\sin x}{3+4\cos^2 x}\,dx$

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29. Q65 2025

    Integrate: $\int \frac{\sin^6 x+\cos^6 x}{\sin^2 x\cos^2 x}\,dx$

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30. Q66 2025

    Integrate: $\int_2^8 |x-5|\,dx$

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31. Q67 2025

    Integrate: $\int_{-\pi/4}^{\pi/4} \sin^2 x\, dx$

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32. Q68 2025

    Integrate: $\int_0^1 x\log(1+2x)\,dx$

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33. Q69 20252025 Set A2025 Set E

    $\int_0^{\pi/2} \frac{\sqrt{\cos x}}{\sqrt{\sin x}+\sqrt{\cos x}}\,dx =$

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34. Q70 2025 Set A2021 Set J2018

    $\int_\alpha^\beta \varphi(x)\,dx + \int_\beta^\alpha \varphi(x)\,dx =$

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35. Q71 2025 Set A2025 Set E

    $\int 2^{x+1}\,dx =$

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36. Q72 2025 Set A2025 Set E

    $\int \dfrac{(\sqrt{x}+1)^2}{x\sqrt{x}+2x+\sqrt{x}}\,dx =$

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37. Q73 2025 Set A2025 Set E

    $\int_{-1}^{1}\sin^{13}x\cos^{12}x\,dx =$

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38. Q74 2025 Set A2025 Set E

    $\int_0^{\pi/2} \sin x \cdot \cos x\,dx$

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39. Q75 2025 Set A2025 Set E

    $\int\frac{dx}{x^2+4}=$

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40. Q76 2025 Set A2025 Set E

    $\int \frac{\cos 2x}{\cos x+\sin x}\,dx =$

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41. Q77 2025 Set A2025 Set E

    $\int \tan(\tan^{-1}x)\,dx =$

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42. Q78 2025 Set A2025 Set E

    $\int \frac{dx}{e^{-x}} =$

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43. Q79 2025 Set A

    $\int \log x^2\,dx =$

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44. Q80 2025 Set A

    $\int (\sin 3x+4\sin^3 x)\,dx =$

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45. Q81 2025 Set A2025 Set E

    $\int_{-1}^{1}\sin^7 x\cos^{13}x\,dx =$

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46. Q82 2025 Set A2025 Set E

    $\int_{0}^{1}\frac{4\tan^{-1}x}{1+x^2}\,dx =$

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47. Q83 2025 Set A

    $\int_0^1 3x^2\,dx =$

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48. Q84 2025 Set A2025 Set E

    $\int_0^a \frac{x\,dx}{2\sqrt{a^2-x^2}} =$

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49. Q85 2025 Set A2025 Set E

    $\int_0^a \frac{dx}{\sqrt{x}} =$

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50. Q86 2025 Set A2025 Set E

    $\int_0^{\pi/2} \log\tan x\,dx =$

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51. Q87 2025 Set A

    $\int_0^1 (x + 2x + 3x^2 + 4x^3)\,dx =$

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52. Q88 2025 Set A2025 Set E

    $\int_{-1}^{1} \sin x \cdot \cos^3 x \, dx =$

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53. Q89 2025 Set A

    $100\int_{0}^{1} x^{99} \, dx =$

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54. Q90 2025 Set A

    $2\int_{1}^{9} \frac{dx}{\sqrt{x}} =$

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55. Q91 2025 Set A2025 Set E

    $\int \frac{dx}{x \log x} =$

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56. Q92 2025 Set A2025 Set E

    $\int \frac{x-3}{x^2-9} \, dx =$

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57. Q93 2025 Set A

    $\int_0^2 e^x\,dx =$

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58. Q94 2025 Set A2025 Set E

    $\int e^{2\log x}\,dx =$

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59. Q95 2025 Set A2025 Set E

    $\int x^m \cdot x^n\,dx =$

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60. Q96 2025 Set A

    $\int e^3 \cdot e^x\,dx =$

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61. Q97 2025 Set E2021 Set I

    $\int_{\alpha}^{\beta}\varphi(x)dx+\int_{\beta}^{\alpha}\varphi(x)dx =$

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62. Q98 2025 Set E

    $\int \log x^{2}\,dx =$

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63. Q99 2025 Set E

    $\int (\sin 3x + 4\sin^{3}x)\,dx =$

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64. Q100 2025 Set E

    $\int_{0}^{1}3x^{2}\,dx =$

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65. Q101 2025 Set E

    $\int e^{3}\cdot e^{x}\,dx =$

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66. Q102 2025 Set E

    $\int_{0}^{2}e^{x}\,dx =$

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67. Q103 2025 Set E

    $\int_0^1 (x+2x+3x^2+4x^3)\,dx =$

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68. Q104 2025 Set E

    $100\int_0^1 x^{99}\,dx =$

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69. Q105 2025 Set E

    $2\int_1^9 \frac{dx}{\sqrt{x}} =$

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