Integrals

JEE Advanced · Mathematics · 61 past questions

42 of 61 · show all

1. Q1 2026 Paper 2

   The value of the definite integral…

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2. Q4 2024 Paper 2

   PARAGRAPH “II”…

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3. Q5 2024 Paper 2

   PARAGRAPH “II”…

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4. 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…

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5. Q7 2022 Paper 1

   Consider the equation…

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6. Q10 2021 Paper 2

   Let $f:\left[-\dfrac{\pi}{2},\dfrac{\pi}{2}\right]\to\mathbb{R}$ be a continuous function such that…

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7. Q12 2021 Paper 2

   Let $g_i:\left[\frac{\pi}{8},\frac{3\pi}{8}\right]\to\mathbb{R}$, $i=1,2$, and…

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8. Q15 2020 Paper 1

   Which of the following inequalities is/are TRUE?

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9. Q16 2020 Paper 2

   Let $f:\mathbb{R}\to\mathbb{R}$ be a differentiable function such that its derivative $f'$ is continuous and…

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10. Q17 2019 Paper 1

    If…

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11. Q18 2019 Paper 2

    For $a \in \mathbb{R}$, $|a|>1$, let…

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12. Q19 2019 Paper 2

    The value of the integral $$\int_0^{\pi/2}…

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13. Q20 2018 Paper 1

    Let $f: [0, \infty) \to \mathbb{R}$ be a continuous function such that…

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14. Q23 2017 Paper 1

    Let $f:\mathbb{R}\to\mathbb{R}$ be a differentiable function such that $f(0)=0$…

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15. Q24 2017 Paper 2

    If $I = \sum_{k=1}^{98} \int_k^{k+1} \frac{k+1}{x(x+1)}\,dx$, then

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16. 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

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17. Q27 2015 Paper 1

    Let $f:\mathbb{R}\to\mathbb{R}$ be a function defined by…

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18. 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…

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19. 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 $\tan^{-1}x$…

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20. 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 $x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$.…

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21. 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…

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22. 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…

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23. 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…

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24. Q37 2014 Paper 1

    The value of…

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25. 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…

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26. 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…

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27. 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…

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28. 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…

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29. Q43 2013 Paper 2

    For $a \in \mathbb{R}$ (the set of all real numbers), $a \neq -1$…

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30. Q44 2012 Paper 1

    The integral $\int \frac{\sec^2 x}{(\sec x+\tan x)^{9/2}}\,dx$ equals (for some arbitrary constant $K$)

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31. 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

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32. Q47 2012 Paper 2

    Paragraph for Questions 51 and 52…

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33. 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

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34. Q49 2011 Paper 1

    The value of…

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35. 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…

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36. Q52 2010 Paper 1

    The value(s) of $\int_0^1 \frac{x^4(1-x)^4}{1+x^2}\,dx$ is (are)

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37. Q54 2009 Paper 2

    If…

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38. Q55 2008 Paper 1

    Let $S_n = \sum_{k=1}^{n} \dfrac{n}{n^2 + kn + k^2}$ and $T_n = \sum_{k=0}^{n-1} \dfrac{n}{n^2 + kn + k^2}$…

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39. Q56 2008 Paper 1

    Paragraph for Question Nos. 18 to 20…

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40. Q57 2008 Paper 2

    Let…

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41. Q59 2007 Paper 1

    Let $F(x)$ be an indefinite integral of $\sin^2 x$.…

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42. Q60 2007 Paper 1

    Match the integrals in Column I with the values in Column II and indicate your answer by darkening the…

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