Integrals

JEE Main · Mathematics · 16 past questions

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6 of 16 · show all

1. 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…

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2. 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…

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3. Q7 2026 4 Apr Shift 2

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

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4. Q8 2026 4 Apr Shift 2

   Let $f$ be a twice differentiable function such that $f(x)=\int_0^x \tan(t-x)\,dt-\int_0^x f(t)\tan t\,dt$…

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5. 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 $f(a)$.…

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6. 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…

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