Integrals

JEE Advanced · Mathematics · 61 past questions

9 of 61 · show all

1. Q27 2015 Paper 1

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

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2. 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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3. 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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4. Q30 2015 Paper 2

   Let $f:\mathbb{R}\to\mathbb{R}$ be a continuous odd function, which vanishes exactly at one point and…

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5. Q31 2015 Paper 2

   The option(s) with the values of $a$ and $L$ that satisfy the following equation…

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6. 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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7. 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…

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8. 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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9. 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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