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← Bihar Board Class 12 PYQ

Integrals

Bihar Board Class 12 · Mathematics · 212 past questions

139 of 212 · show all

  1. Q1 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I
    $\int (x+2)\,dx =$
  2. Q2 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I
    $\int \frac{dx}{x-1} =$
  3. Q4 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int \sin^2\frac{x}{2}\,dx =$
  4. Q6 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B20252019 Set F
    $\int_0^1 \frac{dx}{1+x^2} =$
  5. Q9 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_{-2}^{2} |x|\,dx =$
  6. Q10 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2024 Set J2024 Set D2021 Set J2021 Set I
    $\int \frac{1-\cos 2x}{1+\cos 2x}\,dx =$
  7. Q11 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int e^x\left(\tan^{-1}x + \frac{1}{1+x^2}\right)dx =$
  8. Q12 2026 Set A2026 Set H2026 Set E2026 Set F2026 Set J2026 Set B
    $\int_1^e \frac{(\log x)^2}{x}\,dx =$
  9. Q13 2026 Set A2026 Set H2026 Set E2026 Set F2026 Set J2026 Set B
    $\int_0^{\pi/4} \frac{e^{\tan x}}{\cos^2 x}\,dx =$
  10. Q14 2026 Set A2026 Set H2026 Set E2026 Set F2026 Set J2026 Set B2024 Set J2024 Set D2021 Set J2021 Set I2019 Set F
    $\int_0^{\pi/2} \cos^2 x\,dx =$
  11. Q15 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_0^{2\pi} |\sin x|\,dx =$
  12. Q17 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2016
    $\int \frac{dx}{x^2+a^2} =$
  13. Q18 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I
    $\int \log x\, dx =$
  14. Q20 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_1^4 \frac{dx}{\sqrt{x}} =$
  15. Q24 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set B
    $\int_{-\pi}^{\pi} \sin^5 x\, dx =$
  16. Q27 2026 Set A2026 Set H2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    Solve : $\int_1^2 \frac{\log x}{x}\,dx$.
  17. Q28 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\int_0^a \sqrt{a^2 - x^2}\,dx =$
  18. Q31 2026 Set C2026 Set D
    $\displaystyle\int_1^e \frac{(\log x)^2}{x}\,dx=$
  19. Q32 2026 Set C2026 Set D
    $\displaystyle\int_0^{\pi/4} \frac{e^{\tan x}}{\cos^2 x}\,dx=$
  20. Q34 2026 Set D
    $\cos^2 x\,dx$ integrated from $0$ to $\pi/2$: $\int_0^{\pi/2} \cos^2 x\, dx =$
  21. Q38 2026 Set J
    $\int_{-\pi}^{\pi} \sin^3 x \, dx =$
  22. Q40 2025
    $\int \dfrac{dx}{\sqrt{a^2-x^2}} =$
  23. Q41 2025
    $\int x^2\left(\dfrac{1}{x^2}+1\right)dx =$
  24. Q42 2025
    $\int \dfrac{5-3\sin x}{\cos^2 x}\,dx =$
  25. Q43 2025
    $\int \text{cosec}\,x\,dx =$
  26. Q44 2025
    $\int \dfrac{(7+\log x)^2}{x}\,dx$
  27. Q48 2025
    $\displaystyle\int \frac{\cos\sqrt{x}}{\sqrt{x}}\,dx =$
  28. Q49 2025
    $\int \dfrac{3x^2}{x^6+1}\,dx =$
  29. Q52 2025
    $\int \dfrac{dx}{\sqrt{x^2+a^2}} =$
  30. Q53 2025
    $\int_{-1}^{1} \sin^7 x \cos^6 x\,dx =$
  31. Q54 2025
    $\int_0^{\pi/4} \tan x\,dx =$
  32. Q55 2025
    $\int_2^3 \frac{1}{x}\,dx =$
  33. Q56 2025
    $\int \frac{\sin^{-1}x}{\sqrt{1-x^2}}\,dx$
  34. Q59 2025
    $\displaystyle\int e^{-7x}\, dx =$
  35. Q60 2025
    $\displaystyle\int (5x^4+2x+\sin x)\, dx =$
  36. Q62 2025
    Integrate: $\int \frac{dx}{1+\cos x}$
  37. Q66 2025
    Integrate: $\int_2^8 |x-5|\,dx$
  38. Q70 2025 Set A2021 Set J2018
    $\int_\alpha^\beta \varphi(x)\,dx + \int_\beta^\alpha \varphi(x)\,dx =$
  39. Q71 2025 Set A2025 Set E
    $\int 2^{x+1}\,dx =$
  40. Q73 2025 Set A2025 Set E
    $\int_{-1}^{1}\sin^{13}x\cos^{12}x\,dx =$
  41. Q74 2025 Set A2025 Set E
    $\int_0^{\pi/2} \sin x \cdot \cos x\,dx$
  42. Q75 2025 Set A2025 Set E
    $\int\frac{dx}{x^2+4}=$
  43. Q77 2025 Set A2025 Set E
    $\int \tan(\tan^{-1}x)\,dx =$
  44. Q78 2025 Set A2025 Set E
    $\int \frac{dx}{e^{-x}} =$
  45. Q81 2025 Set A2025 Set E
    $\int_{-1}^{1}\sin^7 x\cos^{13}x\,dx =$
  46. Q83 2025 Set A
    $\int_0^1 3x^2\,dx =$
  47. Q85 2025 Set A2025 Set E
    $\int_0^a \frac{dx}{\sqrt{x}} =$
  48. Q87 2025 Set A
    $\int_0^1 (x + 2x + 3x^2 + 4x^3)\,dx =$
  49. Q88 2025 Set A2025 Set E
    $\int_{-1}^{1} \sin x \cdot \cos^3 x \, dx =$
  50. Q89 2025 Set A
    $100\int_{0}^{1} x^{99} \, dx =$
  51. Q90 2025 Set A
    $2\int_{1}^{9} \frac{dx}{\sqrt{x}} =$
  52. Q91 2025 Set A2025 Set E
    $\int \frac{dx}{x \log x} =$
  53. Q92 2025 Set A2025 Set E
    $\int \frac{x-3}{x^2-9} \, dx =$
  54. Q93 2025 Set A
    $\int_0^2 e^x\,dx =$
  55. Q94 2025 Set A2025 Set E
    $\int e^{2\log x}\,dx =$
  56. Q95 2025 Set A2025 Set E
    $\int x^m \cdot x^n\,dx =$
  57. Q96 2025 Set A
    $\int e^3 \cdot e^x\,dx =$
  58. Q97 2025 Set E2021 Set I
    $\int_{\alpha}^{\beta}\varphi(x)dx+\int_{\beta}^{\alpha}\varphi(x)dx =$
  59. Q100 2025 Set E
    $\int_{0}^{1}3x^{2}\,dx =$
  60. Q101 2025 Set E
    $\int e^{3}\cdot e^{x}\,dx =$
  61. Q102 2025 Set E
    $\int_{0}^{2}e^{x}\,dx =$
  62. Q103 2025 Set E
    $\int_0^1 (x+2x+3x^2+4x^3)\,dx =$
  63. Q104 2025 Set E
    $100\int_0^1 x^{99}\,dx =$
  64. Q105 2025 Set E
    $2\int_1^9 \frac{dx}{\sqrt{x}} =$
  65. Q106 2024 Set D2024 Set J2018
    $\int\sqrt{1+\cos 2x}\,dx=$
  66. Q107 2024 Set D2024 Set J
    $\int (x+\cos 2x)\,dx =$
  67. Q108 2024 Set D2024 Set J
    $\int e^x\left\{\sin^{-1}x+\frac{1}{\sqrt{1-x^2}}\right\}dx =$
  68. Q109 2024 Set D2024 Set J
    $\int \frac{dx}{x(x+2)} =$
  69. Q110 2024 Set D2024 Set J
    $\int \sqrt{a^2-x^2}\,dx =$
  70. Q111 2024 Set D2024 Set J
    $\int_{-\pi/2}^{\pi/2}\sin^7 x\,dx =$
  71. Q113 2024 Set D2024 Set J
    $\int_{-\pi}^{\pi}\tan x\,dx =$
  72. Q115 2024 Set D2024 Set J
    $\int \frac{dx}{2-3x} =$
  73. Q117 2024 Set D
    $\int xe^{x}\,dx =$
  74. Q119 2024 Set D2024 Set J
    $\int\frac{\log x}{x}\,dx =$
  75. Q121 2024 Set D2024 Set J
    $\int\sqrt{\cos x}\cdot\sin x\,dx =$
  76. Q122 2024 Set D2024 Set J2021 Set J2021 Set I
    $\int \cot^2 x\,dx =$
  77. Q123 2024 Set D2024 Set J
    $\int \frac{dx}{a^2+x^2}=$
  78. Q124 2024 Set D2024 Set J
    $\int \sec x\,dx=$
  79. Q126 2024 Set D2024 Set J
    $\int \tan^2 x\,dx=$
  80. Q127 2024 Set D2024 Set J
    $\int_4^9\frac{1}{\sqrt{x}}\,dx =$
  81. Q131 2024 Set J
    $\int xe^x\,dx =$
  82. Q132 2023
    $\displaystyle\int_{\pi/6}^{\pi/6} \tan\theta \, d\theta =$
  83. Q133 2023
    $\int \sin^3\theta \; \text{cosec}^2\theta \, d\theta =$
  84. Q135 2023
    $\int (4\cos x - 5\sin x) \, dx =$
  85. Q137 20232023 Set E
    $\int \frac{3x^2+2}{x^3+2x} \, dx =$
  86. Q138 20232023 Set E
    $\int \frac{dx}{x^2+5} =$
  87. Q140 20232023 Set E
    $\int \sin\frac{3x}{4}\,dx =$
  88. Q141 20232023 Set E
    $\int \cos\frac{7x}{9}\,dx =$
  89. Q142 20232023 Set E
    $\int \sec^2\frac{17x}{23}\,dx =$
  90. Q143 20232023 Set E
    $\int 4^x\,dx =$
  91. Q144 2023
    $\int x(4x^2 - 6)\,dx =$
  92. Q145 20232023 Set E
    $\int e^x(\cos x - \sin x)\,dx =$
  93. Q147 2023
    $\int e^x \left(\dfrac{1}{x} - \dfrac{1}{x^2}\right) dx =$
  94. Q148 20232023 Set E
    $3\int_0^3 x^3\,dx =$
  95. Q149 20232023 Set E
    $\int_{-1}^{1} \sin^{17} x \cos^3 x \, dx =$
  96. Q151 20232023 Set E
    $3 \int \sqrt{x} \, dx =$
  97. Q152 20232023 Set E
    $\int \frac{x+2}{x^2-4} \, dx =$
  98. Q153 20232023 Set E
    $\int \frac{3\,dx}{\sqrt{1-9x^2}} =$
  99. Q154 20232023 Set E
    $25\int \sec 5x \tan 5x \, dx =$
  100. Q155 2023
    $\int \sec^2 4x \, dx =$
  101. Q157 2023 Set E
    $\int x(4x^2-6)\,dx =$
  102. Q158 2023 Set E
    $\int e^x\left(\frac1x-\frac1{x^2}\right)dx =$
  103. Q159 2023 Set E
    $\int_{-1}^{1}x^{17}\cos^{4}x\,dx =$
  104. Q160 2023 Set E
    $\int\sec^{2}4x\,dx =$
  105. Q161 2023 Set E
    $\int_{-\pi/6}^{\pi/6}\tan\theta\,d\theta=$
  106. Q162 2023 Set E
    $\int\sin^3\theta\,\operatorname{cosec}^2\theta\,d\theta=$
  107. Q164 2023 Set E
    $\int(4\cos x-5\sin x)\,dx=$
  108. Q167 2021 Set I
    $\int\frac{x^4-1}{x^2+1}dx=$
  109. Q168 2021 Set J2021 Set I
    $\int_1^3 dx=$
  110. Q169 2021 Set J2021 Set I
    $\int \sin x\cdot\cos x\,dx=$
  111. Q173 2021 Set J2021 Set I
    $\int_0^3 x\,dx =$
  112. Q174 2021 Set J2021 Set I
    $\int_0^2 (x^2+1)\,dx =$
  113. Q175 2021 Set J2021 Set I
    $\int_0^{1} \frac{dx}{x+1} =$
  114. Q176 2021 Set J2021 Set I
    $\int_{-\pi/2}^{\pi/2} |\cos x|\,dx =$
  115. Q177 2021 Set J
    $\int_0^{1} e^x\,dx =$
  116. Q178 2019 Set F
    $\int \frac{dx}{x^2+16} = ?$
  117. Q179 2019 Set F
    $\int_a^b x^2\,dx = ?$
  118. Q180 2019 Set F
    $\int_2^1 \frac{dx}{x} = ?$
  119. Q181 2019 Set F
    $\int_{-\pi/2}^{\pi/2}\sin^9x\,dx=?$
  120. Q182 2019 Set F
    $\int x^n\,dx,\ (n \neq 0) = ?$
  121. Q183 2019 Set F
    $\displaystyle\int\frac{dx}{1+x^2}=\ ?$
  122. Q184 2019 Set F
    $\int \operatorname{cosec}^2 x\,dx = ?$
  123. Q186 2019 Set F
    $\int \sec x\,dx = ?$
  124. Q187 2018
    $\int x^{2}\cdot e^{x^{3}}\,dx=$
  125. Q189 2018
    $\int\dfrac{dx}{a^{2}+x^{2}}=$
  126. Q190 2018
    If $f(-x) = -f(x)$ then $\int_{-a}^{a} f(x)\,dx =$
  127. Q191 2018
    $\int_0^1 x\,dx = ..........$
  128. Q195 2017
    $\int x^5\,dx = $ ............
  129. Q196 2017
    $\int 0\,dx = $ ............
  130. Q197 2017
    $\int \frac{dx}{x} = $ ............
  131. Q198 2017
    $\int_b^a x^3\,dx = $ ........
  132. Q202 2016
    $\int x^8\,dx$
  133. Q203 2016
    The integration of O with respect to x is…
  134. Q205 2016
    $\int_{b}^{a} x^2\,dx$
  135. Q206 2016
    $\int \frac{-1}{1+x^2}dx =$
  136. Q208 2015
    $\int 1\cdot dx$
  137. Q209 2015
    $\int\dfrac{dx}{1+\cos x}=$
  138. Q210 2015
    $\int_a^b x^5\,dx =$
  139. Q211 2015
    If $x>a$, $\displaystyle\int \dfrac{dx}{x^2-a^2} =$