Rewrite: ∫sinxcosxtanxdx=∫tanxsec2xdx. Let u=tanx, du=sec2xdx. Integral becomes ∫udu=2u+c=2tanx+c.
Solution of differential equation xdy−ydx=0 respresents :
Held on 30 May 2023 · Verified 13 Jul 2026.
family of straight lines passing through origin
family of parabolas whose vertex is at origin
family of circles whose centre is at origin
family of straight lines passing through (1, 1)
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The derivative of x³ + 2x² - 5x + 1 is:
For $y \neq 0$, the particular solution of the differential equation $2ye^{x/y}dx + (y - 2xe^{x/y})dy = 0$ at the point (1, 1) is
The value of ∫₀¹ x·eˣ dx is:
Match List-I with List-II | List-I | List-II | | --- | --- | | (A) $f(x) = x \sin x$ | (I) is not continuous at $x = -3$ | | (B) $f(x) = \frac{\vert x\vert }{x}, x \neq 0$ and $f(x) = 1 \text{ at } x = 0$ | (II) is continuous everywhere | | (C) $f(x) = x - [x]$, $[x]$ denotes greatest integer function | (III) is not differentiable at $x = 1$ | | (D) $f(x) = e^{\vert x - 1\vert }$ | (IV) is not continuous at $x = 0$ | Choose the correct answer from the options given below:
The area (in sq. units) of the region enclosed by the curve $9x^2 + 4y^2 = 36$ is
Work through every CUET UG Calculus PYQ, year by year.