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.

Q1 2026 2 Apr Shift 1

Let $[\cdot]$ denote the greatest integer function. Then the value of…
Q2 2026 2 Apr Shift 1

If $\alpha=\int_0^{2\sqrt3}\log_2(x^2+4)\,dx+\int_2^4\sqrt{2^x-4}\,dx$, then $\alpha^2$ is equal to…
Q3 2026 2 Apr Shift 2

The value of $\int_0^{20\pi}(\sin^4 x+\cos^4 x)\,dx$ is equal to…
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…
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…
Q6 2026 4 Apr Shift 1

Let $\int_{-2}^{2}\left(|\sin x|+[x\sin x]\right)dx=2(3-\cos 2)+\beta$, where $[\cdot]$ is the greatest…
Q7 2026 4 Apr Shift 2

The integral $\int_0^1 \cot^{-1}\left(1+x+x^2\right)dx$ is equal to…
Q8 2026 4 Apr Shift 2

Let $f$ be a twice differentiable function such that $f(x)=\int_0^x \tan(t-x)\,dt-\int_0^x f(t)\tan t\,dt$…
Q9 2026 5 Apr Shift 1

The value of the integral $\int_0^\infty \frac{\log_e(x)}{x^2+4}\,dx$ is…
Q10 2026 5 Apr Shift 1

The value of the integral $\int_{\pi/6}^{\pi/3}\left(\frac{4-\operatorname{cosec}^{2}x}{\cos^{4}x}\right)dx$…
Q11 2026 5 Apr Shift 2

Let $(2^{1-a} + 2^{1+a})$, $f(a)$, $(3^a + 3^{-a})$ be in A.P. and $\alpha$ be the minimum value of $f(a)$.…
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…
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…
Q14 2026 8 Apr Shift 2

The value of the integral $\int_0^2 \frac{\sqrt{x(x^2+x+1)}}{(\sqrt{x+1})(\sqrt{x^4+x^2+1})}\,dx$ is equal to…
Q15 2026 8 Apr Shift 2

Let $f(x)=\begin{cases}\dfrac13, & x\le \pi/2\\[4pt] \dfrac{b(1-\sin x)}{(\pi-2x)^2}, & x>\pi/2\end{cases}$.…
Q16 2026 8 Apr Shift 2

If…