Integrals

JEE Main · Mathematics · 16 past questions

These are the board's own papers. 330 more board questions reprinted in the books we use in class are for signed-in students: sign in.

9 of 16 · show all

1. Q1 2026 2 Apr Shift 1

   Let $[\cdot]$ denote the greatest integer function. Then the value of…

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2. Q4 2026 2 Apr Shift 2

   Let $f(x)=\int\left(\frac{16x+24}{x^2+2x-15}\right)dx$. If $f(4)=14\log_e(3)$ and…

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3. Q5 2026 4 Apr Shift 1

   Let $f$ be a real polynomial of degree $n$ such that $f(x)=f'(x)f''(x)$, for all $x\in\mathbb{R}$. If…

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4. Q9 2026 5 Apr Shift 1

   The value of the integral $\int_0^\infty \frac{\log_e(x)}{x^2+4}\,dx$ is…

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5. Q10 2026 5 Apr Shift 1

   The value of the integral $\int_{\pi/6}^{\pi/3}\left(\frac{4-\operatorname{cosec}^{2}x}{\cos^{4}x}\right)dx$…

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6. Q12 2026 6 Apr Shift 1

   The value of the integral $\int_{-\pi/4}^{\pi/4}\left(\frac{32\cos^4 x}{1+e^{\sin x}}\right)dx$ is…

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7. Q13 2026 6 Apr Shift 2

   The value of the integral $\int_{-1}^{1} \left(\frac{x^3 + |x| + 1}{x^2 + 2|x| + 1}\right) dx$ is equal to…

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8. Q15 2026 8 Apr Shift 2

   Let $f(x)=\begin{cases}\dfrac13, & x\le \pi/2\\[4pt] \dfrac{b(1-\sin x)}{(\pi-2x)^2}, & x>\pi/2\end{cases}$.…

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9. Q16 2026 8 Apr Shift 2

   If…

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