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Integrals

JEE Advanced · Mathematics · 61 past questions

  1. Q1 2026 Paper 2
    The value of the definite integral…
  2. Q2 2025 Paper 2
    If…
  3. Q3 2024 Paper 2
    Let the function $f:[1,\infty)\to\mathbb{R}$ be defined by…
  4. Q4 2024 Paper 2
    PARAGRAPH “II”…
  5. Q5 2024 Paper 2
    PARAGRAPH “II”…
  6. Q6 2023 Paper 2
    For $x \in \mathbb{R}$, let $\tan^{-1}(x) \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. Then the minimum…
  7. Q7 2022 Paper 1
    Consider the equation…
  8. Q8 2022 Paper 2
    The greatest integer less than or equal to…
  9. Q9 2022 Paper 2
    For positive integer $n$, define…
  10. Q10 2021 Paper 2
    Let $f:\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]\to\mathbb{R}$ be a continuous function such that…
  11. Q11 2021 Paper 2
    Let $g_i:\left[\frac{\pi}{8},\frac{3\pi}{8}\right]\to\mathbb{R}$, $i=1,2$, and…
  12. Q12 2021 Paper 2
    Let $g_i:\left[\frac{\pi}{8},\frac{3\pi}{8}\right]\to\mathbb{R}$, $i=1,2$, and…
  13. Q13 2021 Paper 2
    Paragraph…
  14. Q14 2021 Paper 2
    For any real number $x$, let $[x]$ denote the largest integer less than or equal to $x$. If…
  15. Q15 2020 Paper 1
    Which of the following inequalities is/are TRUE?
  16. Q16 2020 Paper 2
    Let $f:\mathbb{R}\to\mathbb{R}$ be a differentiable function such that its derivative $f'$ is continuous and…
  17. Q17 2019 Paper 1
    If…
  18. Q18 2019 Paper 2
    For $a \in \mathbb{R}$, $|a|>1$, let…
  19. Q19 2019 Paper 2
    The value of the integral $$\int_0^{\pi/2}…
  20. Q20 2018 Paper 1
    Let $f: [0, \infty) \to \mathbb{R}$ be a continuous function such that…
  21. Q21 2018 Paper 1
    For each positive integer $n$, let…
  22. Q22 2018 Paper 2
    The value of the integral…
  23. Q23 2017 Paper 1
    Let $f:\mathbb{R}\to\mathbb{R}$ be a differentiable function such that $f(0)=0$…
  24. Q24 2017 Paper 2
    If $I = \sum_{k=1}^{98} \int_k^{k+1} \frac{k+1}{x(x+1)}\,dx$, then
  25. Q25 2016 Paper 1
    The total number of distinct $x \in [0, 1]$ for which $\int_0^x \frac{t^2}{1+t^4}\,dt = 2x - 1$ is
  26. Q26 2016 Paper 2
    The value of $\int_{-\pi/2}^{\pi/2} \frac{x^2 \cos x}{1+e^x}\,dx$ is equal to
  27. Q27 2015 Paper 1
    Let $f:\mathbb{R}\to\mathbb{R}$ be a function defined by…
  28. Q28 2015 Paper 1
    Let $F(x)=\int_x^{x^2+\frac{\pi}{6}}2\cos^2 t\,dt$ for all $x\in\mathbb{R}$ and…
  29. Q29 2015 Paper 2
    If $\alpha = \int_0^1 \left(e^{9x+3\tan^{-1}x}\right)\left(\frac{12+9x^2}{1+x^2}\right)dx$ where $\tan^{-1}x$…
  30. Q30 2015 Paper 2
    Let $f:\mathbb{R}\to\mathbb{R}$ be a continuous odd function, which vanishes exactly at one point and…
  31. Q31 2015 Paper 2
    The option(s) with the values of $a$ and $L$ that satisfy the following equation…
  32. Q32 2015 Paper 2
    Let $f(x)=7\tan^8 x+7\tan^6 x-3\tan^4 x-3\tan^2 x$ for all $x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$.…
  33. Q33 2015 Paper 2
    Let $f'(x)=\dfrac{192x^3}{2+\sin^4\pi x}$ for all $x\in\mathbb{R}$ with $f\left(\frac12\right)=0$. If…
  34. Q34 2015 Paper 2
    Let $F:\mathbb{R}\to\mathbb{R}$ be a thrice differentiable function. Suppose that $F(1)=0$, $F(3)=-4$ and…
  35. Q35 2015 Paper 2
    Let $F:\mathbb{R}\to\mathbb{R}$ be a thrice differentiable function. Suppose that $F(1)=0$, $F(3)=-4$ and…
  36. Q36 2014 Paper 1
    Let $f:[a,b]\to[1,\infty)$ be a continuous function and let $g:\mathbb{R}\to\mathbb{R}$ be defined as…
  37. Q37 2014 Paper 1
    The value of…
  38. Q38 2014 Paper 2
    The following integral…
  39. Q39 2014 Paper 2
    Let $f:[0,2]\to\mathbb{R}$ be a function which is continuous on $[0,2]$ and is differentiable on $(0,2)$ with…
  40. Q40 2014 Paper 2
    Given that for each $a \in (0,1)$, $\lim_{h\to 0^+}\int_h^{1-h} t^{-a}(1-t)^{a-1}\,dt$ exists. Let this limit…
  41. Q41 2014 Paper 2
    Given that for each $a \in (0,1)$, $\lim_{h\to 0^+}\int_h^{1-h} t^{-a}(1-t)^{a-1}\,dt$ exists. Let this limit…
  42. Q42 2013 Paper 1
    Let $f: \left[\frac{1}{2}, 1\right] \to \mathbb{R}$ (the set of all real numbers) be a positive, non-constant…
  43. Q43 2013 Paper 2
    For $a \in \mathbb{R}$ (the set of all real numbers), $a \neq -1$…
  44. Q44 2012 Paper 1
    The integral $\int \frac{\sec^2 x}{(\sec x+\tan x)^{9/2}}\,dx$ equals (for some arbitrary constant $K$)
  45. Q45 2012 Paper 1
    Let $S$ be the area of the region enclosed by $y=e^{-x^2}$, $y=0$, $x=0$, and $x=1$. Then
  46. Q46 2012 Paper 2
    The value of the integral $\int_{-\pi/2}^{\pi/2} \left(x^2 + \ln\frac{\pi + x}{\pi - x}\right)\cos x \, dx$ is
  47. Q47 2012 Paper 2
    Paragraph for Questions 51 and 52…
  48. Q48 2012 Paper 2
    If $f(x)=\int_0^x e^{t^2}(t-2)(t-3)\,dt$ for all $x\in(0,\infty)$, then
  49. Q49 2011 Paper 1
    The value of…
  50. Q50 2011 Paper 2
    Let $f:[-1,2]\to[0,\infty)$ be a continuous function such that $f(x)=f(1-x)$ for all $x\in[-1,2]$. Let…
  51. Q51 2010 Paper 1
    The value of $\lim_{x\to0}\frac{1}{x^3}\int_0^x\frac{t\ln(1+t)}{t^4+4}\,dt$ is
  52. Q52 2010 Paper 1
    The value(s) of $\int_0^1 \frac{x^4(1-x)^4}{1+x^2}\,dx$ is (are)
  53. Q53 2010 Paper 1
    For any real number x, let [x] denote the largest integer less than or equal to x. Let f be a real valued…
  54. Q54 2009 Paper 2
    If…
  55. Q55 2008 Paper 1
    Let $S_n = \sum_{k=1}^{n} \dfrac{n}{n^2 + kn + k^2}$ and $T_n = \sum_{k=0}^{n-1} \dfrac{n}{n^2 + kn + k^2}$…
  56. Q56 2008 Paper 1
    Paragraph for Question Nos. 18 to 20…
  57. Q57 2008 Paper 2
    Let…
  58. Q58 2007 Paper 1
    $\displaystyle\lim_{x \to \frac{\pi}{4}} \dfrac{\int_2^{\sec^2 x} f(t)\,dt}{x^2 - \dfrac{\pi^2}{16}}$ equals
  59. Q59 2007 Paper 1
    Let $F(x)$ be an indefinite integral of $\sin^2 x$.…
  60. Q60 2007 Paper 1
    Match the integrals in Column I with the values in Column II and indicate your answer by darkening the…
  61. Q61 2007 Paper 2
    Let $f(x) = \dfrac{x}{(1+x^n)^{1/n}}$ for $n \ge 2$ and $g(x) = (f \circ f \circ \cdots \circ f)(x)$, where…