JEE MAIN Area Enclosed Between The Curves Definite Integration Previous Year Questions (PYQs) – Page 1 of 7

JEE MAIN Area Enclosed Between The Curves Definite Integration Previous Year Questions (PYQs) – Page 1 of 7

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The integral $\displaystyle \int_{0}^{\pi}\sqrt{1+4\sin^{2}\frac{x}{2}-4\sin\frac{x}{2}}\,dx$ equals:

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The area of the region described by $A=\{(x,y):x^{2}+y^{2}\le 1 \text{ and } y^{2}\le 1-x\}$ is :

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If the area (in sq. units) bounded by the parabola $y^{2}=4\lambda x$ and the line $y=\lambda x,\ \lambda>0$, is $\dfrac{1}{9}$, then $\lambda$ is equal to:

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The area of the region given by $\{(x,y):\, xy\le 8,\ 1\le y\le x^{2}\}$ is:

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If the area of the region $\left\{(x, y):-1 \leq x \leq 1,0 \leq y \leq \mathrm{a}+\mathrm{e}^{|x|}-\mathrm{e}^{-x}, \mathrm{a}>0\right\}$ is $\frac{\mathrm{e}^2+8 \mathrm{e}+1}{\mathrm{e}}$, then the value of $a$ is

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A line passing through the point $A(-2,0)$ touches the parabola $P: y^2=x-2$ at the point $B$ in the first quadrant. The area of the region bounded by the line $\overline{AB}$, parabola $P$ and the $x$-axis is:

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$ \text{The area bounded by the curves } y=\lvert x^{2}-1\rvert \text{ and } y=1 \text{ is :}$

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The area (in square units) bounded by the curves $y=\sqrt{x}$, $2y-x+3=0$, $x$-axis, and lying in the first quadrant is :

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The area (in sq. units) of the region bounded by the curve $x^2=4y$ and the straight line $x=4y-2$ is :

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The area (in sq. units) of the region ${(x,y)\in \mathbb{R}^{2} : x \ge 0,\ y \ge 0,\ y \ge x-2 \text{ and } y \le \sqrt{x}}$ is :

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