Integrals

Bihar Board Class 12 · Mathematics · 212 past questions

24 of 212 · show all

1. 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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2. Q39 2025

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

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3. Q45 2025

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

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4. Q46 2025

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

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5. Q47 2025

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

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6. Q50 2025

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

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7. Q51 2025

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

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8. Q57 2025

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

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9. Q58 2025

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

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10. Q61 2025

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

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11. 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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12. Q64 2025

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

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13. Q65 2025

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

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14. Q67 2025

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

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15. 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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16. Q72 2025 Set A2025 Set E

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

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17. Q76 2025 Set A2025 Set E

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

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18. Q79 2025 Set A

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

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19. Q80 2025 Set A

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

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20. Q82 2025 Set A2025 Set E

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

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21. Q84 2025 Set A2025 Set E

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

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22. Q86 2025 Set A2025 Set E

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

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23. Q98 2025 Set E

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

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24. Q99 2025 Set E

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

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