Integrals

Bihar Board Class 12 · Mathematics · 212 past questions

34 of 212 · show all

1. Q9 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $\int_{-2}^{2} |x|\,dx =$

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2. Q15 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $\int_0^{2\pi} |\sin x|\,dx =$

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3. Q16 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2024 Set J2024 Set D

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

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4. Q23 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

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

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5. Q24 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set B

   $\int_{-\pi}^{\pi} \sin^5 x\, dx =$

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6. Q37 2026 Set J2026 Set C2026 Set B2026 Set H

   Prove that $\int_0^{\pi/2} (\sqrt{\tan x} + \sqrt{\cot x})\, dx = \pi\sqrt{2}$.

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7. Q38 2026 Set J

   $\int_{-\pi}^{\pi} \sin^3 x \, dx =$

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8. Q53 2025

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

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9. Q57 2025

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

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10. Q66 2025

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

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11. 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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12. Q70 2025 Set A2021 Set J2018

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

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13. Q73 2025 Set A2025 Set E

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

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14. Q81 2025 Set A2025 Set E

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

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15. Q86 2025 Set A2025 Set E

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

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16. Q88 2025 Set A2025 Set E

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

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17. Q97 2025 Set E2021 Set I

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

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18. Q111 2024 Set D2024 Set J

    $\int_{-\pi/2}^{\pi/2}\sin^7 x\,dx =$

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19. Q113 2024 Set D2024 Set J

    $\int_{-\pi}^{\pi}\tan x\,dx =$

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20. Q128 2024 Set D2024 Set J

    Evaluate : $\int_0^{\pi/2}\log\cos x\,dx$.

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21. Q132 2023

    $\displaystyle\int_{\pi/6}^{\pi/6} \tan\theta \, d\theta =$

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22. Q139 20232023 Set E

    $\int_{-1}^{1} \log\left(\frac{3+x}{3-x}\right) \, dx =$

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23. Q149 20232023 Set E

    $\int_{-1}^{1} \sin^{17} x \cos^3 x \, dx =$

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24. Q150 2023

    $\int_{-1}^{1} x^{17} \, x \, dx =$

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25. Q159 2023 Set E

    $\int_{-1}^{1}x^{17}\cos^{4}x\,dx =$

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26. Q161 2023 Set E

    $\int_{-\pi/6}^{\pi/6}\tan\theta\,d\theta=$

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27. Q170 2021 Set J2021 Set I

    $\int_0^{\pi/2} \log\cot\theta\,d\theta =$

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28. Q171 2021 Set J2021 Set I

    $\int_0^{\pi/2} \frac{\cos\theta}{\cos\theta+\sin\theta}\,d\theta =$

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29. Q176 2021 Set J2021 Set I

    $\int_{-\pi/2}^{\pi/2} |\cos x|\,dx =$

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30. Q180 2019 Set F

    $\int_2^1 \frac{dx}{x} = ?$

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31. Q181 2019 Set F

    $\int_{-\pi/2}^{\pi/2}\sin^9x\,dx=?$

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32. Q190 2018

    If $f(-x) = -f(x)$ then $\int_{-a}^{a} f(x)\,dx =$

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33. Q194 2018

    Prove that $\int_0^{2\pi} |\cos x|\,dx = 4$

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34. Q207 2016

    Prove that $\int_0^{\pi/2} \log \sin x\,dx = \int_0^{\pi/2} \log \cos x\,dx = -\frac{\pi}{2}\log 2$

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