Integrals

CBSE Class 12 · Mathematics · 54 past questions

35 of 54 · show all

1. Q3 2026

   Evaluate : $\displaystyle\int_0^1 x\tan^{-1}x\,dx$.

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2. Q4 2026

   Find $\displaystyle\int\sqrt{\dfrac{x+2}{x-2}}\,dx$

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3. Q6 2026

   Find : $\displaystyle\int \dfrac{x + 2}{\sqrt{9x - x^2}}\, dx$

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4. Q7 2026

   (a) Evaluate : $\displaystyle\int_{\pi/12}^{5\pi/12} \dfrac{dx}{1 + \sqrt{\cot x}}$

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5. Q8 2026

   If $\dfrac{d}{dx}(F(x)) = \dfrac{1}{e^x + 1}$, then find $F(x)$ given that $F(0) = \log \dfrac{1}{2}$.

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6. Q9 2026

   $\int \frac{dx}{2^x + 2^{-x}}$ is equal to…

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7. Q11 2026

   Find…

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8. Q12 2026

   Evaluate: $\int_0^{\pi} \frac{\sin^{2026}x}{\sin^{2026}x + \cos^{2026}x}\,dx$

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9. Q13 2026

   Find: $\int \frac{\cos x}{(2+\sin x)(4+\sin x)}\,dx$

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10. Q16 2025

    Find : $\int \frac{x+\sin x}{1+\cos x}\,dx$

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11. Q18 2025

    Evaluate : $\int_0^{\pi/4} \sqrt{1+\sin 2x}\,dx$

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12. Q20 2025

    Find : $\int \frac{x^2+x+1}{(x+2)(x^2+1)}\,dx$.

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13. Q21 2025

    $\int \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha}\,dx$ is equal to…

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14. Q22 2025

    The value of $\int_0^1 \frac{dx}{e^x + e^{-x}}$ is…

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15. Q23 2025

    Evaluate…

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16. Q27 2024

    Find…

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17. Q28 2024

    Evaluate…

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18. Q30 2024

    Evaluate…

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19. Q31 2024

    Find : $\int \frac{x^2+1}{(x^2+2)(x^2+4)}\,dx$

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20. Q32 2024

    Find : $\int \frac{2+\sin 2x}{1+\cos 2x}\,e^x\,dx$

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21. Q33 2024

    $\int_0^{\pi/2} \frac{\sin x-\cos x}{1+\sin x\cos x}\,dx$ is equal to…

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22. Q35 2024

    Evaluate : $\int_{-2}^{2}\sqrt{\frac{2-x}{2+x}}\,dx$

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23. Q38 2023

    $\int \frac{2\cos 2x - 1}{1 + 2\sin x}\,dx$ is equal to…

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24. Q39 2023

    Evaluate…

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25. Q40 2023

    Evaluate…

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26. Q44 2023

    Evaluate : $\int_0^{\pi/2} [\log(\sin x) - \log(2\cos x)]\,dx$.

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27. Q45 2023

    Find…

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28. Q46 2023

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

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29. Q48 2023

    Anti-derivative of $\frac{\tan x - 1}{\tan x + 1}$ with respect to $x$ is

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30. Q49 2023

    Evaluate $\int_0^{\pi/4} \log(1 + \tan x)\, dx$.

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31. Q50 2023

    Find $\int e^{\cot^{-1}x}\left(\frac{1-x+x^2}{1+x^2}\right)dx$.

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32. Q51 2023

    Evaluate $\int_{\log\sqrt{2}}^{\log\sqrt{3}} \frac{1}{(e^x+e^{-x})(e^x-e^{-x})}\,dx$

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33. Q52 2022

    If $\frac{d}{dx}[F(x)]=\frac{\sec^4 x}{\operatorname{cosec}^4 x}$ and…

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34. Q53 2022

    Find : $\int\frac{dx}{\sqrt{x}+\sqrt[3]{x}}$.

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35. Q54 2022

    Evaluate : $\int_0^{\pi} \frac{x}{1+\sin x}\,dx$.

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