JEE Main Mathematics — Calculus previous year questions with solutions.
A function $y=f(x)$ satisfies $f(x)\mathrm{sin}2x+\mathrm{sin}x-(1+{\mathrm{cos}}^{2}x){f}^{'}(x)=0$ with condition $f(0)=0$. Then $f(\frac{\pi }{2})$ is equal to
The value of the integral ${\int }_{1}^{2}(\frac{{t}^{4}+1}{{t}^{6}+1})dt$ is :
The value of the integral ${\int }_{1/2}^{2}\frac{{\mathrm{tan}}^{-1}x}{x}dx$ is equal to
The value of the integral ${\int }_{-{\mathrm{log}}_{e}2}^{{\mathrm{log}}_{e}2}{e}^{x}({\mathrm{log}}_{e}({e}^{x}+\sqrt{1+{e}^{2x}}))dx$ is equal to
The value of the integral ${\int }_{-\frac{\pi }{4}}^{\frac{\pi }{4}}\frac{x+\frac{\pi }{4}}{2-\mathrm{cos}2x}dx$ is :
The value of $\frac{{e}^{-\frac{\pi }{4}}+{\int }_{0}^{\frac{\pi }{4}}{e}^{-x}\mathrm{tan}{}^{50}xdx}{{\int }_{0}^{\frac{\pi }{4}}{e}^{-x}({\mathrm{tan}}^{49}x+{\mathrm{tan}}^{51}x)dx}$
The value of $\frac{8}{\pi }{\int }_{0}^{\frac{\pi }{2}}\frac{{(\mathrm{cos}x)}^{2023}}{{(\mathrm{sin}x)}^{2023}+{(\mathrm{cos}x)}^{2023}}dx$ is ______.
The value of $12{\int }_{0}^{3}|{x}^{2}-3x+2|\mathrm{dx}$ is ______
The value of $\underset{n\rightarrow \infty }{\mathrm{lim}}\frac{1+2-3+4+5-6+\ldots +(3n-2)+(3n-1)-3n}{\sqrt{2{n}^{4}+4n+3-}\sqrt{{n}^{4}+5n+4}}$ is
The value of ${\int }_{\frac{\pi }{3}}^{\frac{\pi }{2}}\frac{(2+3\mathrm{sin}x)}{\mathrm{sin}x(1+\mathrm{cos}x)}dx$ is equal to
The sum of the abosolute maximum and minimum values of the function $f(x)=|{x}^{2}-5x+6|-3x+2$ in the interval $[-1,3]$ is equal to :
The solution of the differential equation $\frac{dy}{dx}=-(\frac{{x}^{2}+3{y}^{2}}{3{x}^{2}+{y}^{2}}),y(1)=0$ is
The slope of tangent at any point $(x,y)$ on a curve $y=y(x)$ is $\frac{{x}^{2}+{y}^{2}}{2xy},x>0$. If $y(2)=0$, then a value of $y(8)$ is
The set of values of $a$ for which $\underset{x\rightarrow a}{\mathrm{lim}}([x-5]-[2x+2])=0$, where, $[\zeta ]$ denotes the greatest integer less than or equal to $\zeta$ is equal to
The set of all $a\in \mathbb{R}$ for which the equation $x|x-1|+|x+2|+a=0$ has exactly one real root, is
The number of points, where the curve $y={x}^{5}-20{x}^{3}+50x+2$ crosses the $x$-axis, is _____.
The minimum value of the function $f(x)={\int }_{0}^{2}{e}^{|x-t|}dt$ is
The integral $16{\int }_{1}^{2}\frac{dx}{{x}^{3}{({x}^{2}+2)}^{2}}$ is equal to
The integral $\int ({(\frac{x}{2})}^{x}+{(\frac{2}{x})}^{x}){\mathrm{log}}_{2}xdx$ is equal to
The area of the region ${(x,y):{x}^{2}\leq y\leq 8-{x}^{2},y\leq 7}$ is
The area of the region $x,y:{x}^{2}\leq y\leq |{x}^{2}-4|,y\geq 1$ is
The area of the region given by ${(x,y):xy\leq 8,1\leq y\leq {x}^{2}}$ is :
The area of the region enclosed by the curve $y={x}^{3}$ and its tangent at the point $(–1,–1)$ is
The area of the region enclosed by the curve $f(x)=\mathrm{max}{\mathrm{sin}x,\mathrm{cos}x},-\pi \leq x\leq \pi$ and the $x-$axis is