Integrals

Bihar Board Class 12 · Mathematics · 212 past questions

50 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. Q7 2026 Set A2026 Set H2026 Set E2026 Set F2026 Set J2026 Set B

   $\int_0^1 \frac{x^3\,dx}{1+x^8} =$

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3. Q8 2026 Set A

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

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4. Q12 2026 Set A2026 Set H2026 Set E2026 Set F2026 Set J2026 Set B

   $\int_1^e \frac{(\log x)^2}{x}\,dx =$

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5. Q13 2026 Set A2026 Set H2026 Set E2026 Set F2026 Set J2026 Set B

   $\int_0^{\pi/4} \frac{e^{\tan x}}{\cos^2 x}\,dx =$

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6. Q14 2026 Set A2026 Set H2026 Set E2026 Set F2026 Set J2026 Set B2024 Set J2024 Set D2021 Set J2021 Set I2019 Set F

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

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7. Q19 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $\int_0^1 \frac{e^{\sqrt{x}}}{\sqrt{x}}\,dx =$

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8. Q20 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $\int_1^4 \frac{dx}{\sqrt{x}} =$

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9. Q22 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $\int_0^{\pi/3} \cos^3 x\, dx =$

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10. Q27 2026 Set A2026 Set H2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

    Solve : $\int_1^2 \frac{\log x}{x}\,dx$.

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11. Q30 2026 Set C2026 Set D

    $\displaystyle\int_0^1 \frac{x^3\,dx}{1+x^8}=$

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12. Q31 2026 Set C2026 Set D

    $\displaystyle\int_1^e \frac{(\log x)^2}{x}\,dx=$

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13. Q32 2026 Set C2026 Set D

    $\displaystyle\int_0^{\pi/4} \frac{e^{\tan x}}{\cos^2 x}\,dx=$

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14. Q34 2026 Set D

    $\cos^2 x\,dx$ integrated from $0$ to $\pi/2$: $\int_0^{\pi/2} \cos^2 x\, dx =$

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15. Q35 2026 Set E

    Solve: $\int_1^2\frac{\log x}{x}dx$.

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16. 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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17. Q54 2025

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

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18. Q55 2025

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

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19. 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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20. Q67 2025

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

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21. Q74 2025 Set A2025 Set E

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

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22. Q82 2025 Set A2025 Set E

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

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23. Q83 2025 Set A

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

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24. Q84 2025 Set A2025 Set E

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

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25. Q85 2025 Set A2025 Set E

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

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26. Q87 2025 Set A

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

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27. Q89 2025 Set A

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

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28. Q90 2025 Set A

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

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29. Q93 2025 Set A

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

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30. Q100 2025 Set E

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

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31. Q102 2025 Set E

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

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32. Q103 2025 Set E

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

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33. Q104 2025 Set E

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

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34. Q105 2025 Set E

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

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35. Q112 2024 Set D2024 Set J

    $\int_0^{\pi/6}\cos x\cdot\cos 2x\,dx =$

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36. Q127 2024 Set D2024 Set J

    $\int_4^9\frac{1}{\sqrt{x}}\,dx =$

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37. Q148 20232023 Set E

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

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38. Q168 2021 Set J2021 Set I

    $\int_1^3 dx=$

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39. Q173 2021 Set J2021 Set I

    $\int_0^3 x\,dx =$

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40. Q174 2021 Set J2021 Set I

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

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41. Q175 2021 Set J2021 Set I

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

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42. Q177 2021 Set J

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

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43. Q179 2019 Set F

    $\int_a^b x^2\,dx = ?$

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44. Q185 2019 Set F

    $\int_0^{\pi/2} \sin^3 x \cos x\,dx = ?$

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45. Q191 2018

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

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46. Q198 2017

    $\int_b^a x^3\,dx = $ ........

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47. Q200 2017

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

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48. Q205 2016

    $\int_{b}^{a} x^2\,dx$

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49. Q210 2015

    $\int_a^b x^5\,dx =$

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50. Q212 2015

    Evaluate $\int_0^{\pi/4} \sin^2 x\,dx$

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