If the solution curve y=f(x) of the differential equation
(x2−4)y′−2xy+2x(4−x2)2=0,x>2,
passes through the point (3,15), then the local maximum value of f is ____.
Held on 23 Jan 2026 · Verified 6 Jul 2026.
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Let $f: [1, \infty) \rightarrow \mathbf{R}$ be a differentiable function defined as $f(x) = \int_1^x f(t)\,dt + (1-x)(\log_e x - 1) + e$. Then the value of $f(f(1))$ is :
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If $\displaystyle\int_{\pi/6}^{\pi/4}\left(\cot\left(x-\dfrac{\pi}{3}\right)\cot\left(x+\dfrac{\pi}{3}\right)+1\right)dx = \alpha\log_e(\sqrt{3}-1)$, then $9\alpha^2$ is equal to ________.
The value of the integral $\displaystyle\int_{0}^{2} \dfrac{\sqrt{x(x^2+x+1)}}{(\sqrt{x+1})(\sqrt{x^4+x^2+1})} \, dx$ is equal to:
The value of the integral $\displaystyle\int_0^\infty \dfrac{\log_e(x)}{x^2 + 4}\,dx$ is:
Work through every JEE Main Calculus PYQ, year by year.