Integrals

Bihar Board Class 12 · Mathematics · 212 past questions

35 of 212 · show all

1. Q132 2023

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

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2. Q133 2023

   $\int \sin^3\theta \; \text{cosec}^2\theta \, d\theta =$

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3. Q134 2023

   $\int (\cos\theta \, \text{cosec}^2\theta - \cos\theta \, \cot^2\theta) \, d\theta =$

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4. Q135 2023

   $\int (4\cos x - 5\sin x) \, dx =$

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5. Q136 2023

   $\int \frac{3\cos x - 2\sin x}{2\cos x + 3\sin x} \, dx =$

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6. Q137 20232023 Set E

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

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7. Q138 20232023 Set E

   $\int \frac{dx}{x^2+5} =$

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8. Q139 20232023 Set E

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

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9. Q140 20232023 Set E

   $\int \sin\frac{3x}{4}\,dx =$

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10. Q141 20232023 Set E

    $\int \cos\frac{7x}{9}\,dx =$

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11. Q142 20232023 Set E

    $\int \sec^2\frac{17x}{23}\,dx =$

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12. Q143 20232023 Set E

    $\int 4^x\,dx =$

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13. Q144 2023

    $\int x(4x^2 - 6)\,dx =$

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14. Q145 20232023 Set E

    $\int e^x(\cos x - \sin x)\,dx =$

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15. Q146 20232023 Set E

    $\int e^x (x^3+3x^2)\,dx =$

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16. Q147 2023

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

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17. Q148 20232023 Set E

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

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18. Q149 20232023 Set E

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

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19. Q150 2023

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

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20. Q151 20232023 Set E

    $3 \int \sqrt{x} \, dx =$

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21. Q152 20232023 Set E

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

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22. Q153 20232023 Set E

    $\int \frac{3\,dx}{\sqrt{1-9x^2}} =$

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23. Q154 20232023 Set E

    $25\int \sec 5x \tan 5x \, dx =$

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24. Q155 2023

    $\int \sec^2 4x \, dx =$

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25. Q156 20232023 Set E

    $\int \frac{dx}{1+36x^2} =$

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26. Q157 2023 Set E

    $\int x(4x^2-6)\,dx =$

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27. Q158 2023 Set E

    $\int e^x\left(\frac1x-\frac1{x^2}\right)dx =$

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28. Q159 2023 Set E

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

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29. Q160 2023 Set E

    $\int\sec^{2}4x\,dx =$

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30. Q161 2023 Set E

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

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31. Q162 2023 Set E

    $\int\sin^3\theta\,\operatorname{cosec}^2\theta\,d\theta=$

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32. Q163 2023 Set E

    $\int(\cos\theta\operatorname{cosec}^2\theta-\cos\theta\cot^2\theta)\,d\theta=$

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33. Q164 2023 Set E

    $\int(4\cos x-5\sin x)\,dx=$

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34. Q165 2023 Set E

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

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35. Q166 2023 Set E

    Find the value of $\int_1^2\left(\frac1x-\frac1{2x^2}\right)e^{2x}\,dx$.

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