Embibe Experts Solutions for Chapter: Application of Integrals, Exercise 2: Exercise 2

The area $\left(\mathrm{in} \mathrm{sq}. \mathrm{units}\right)$ of the region bounded by $x=a\cos \theta$ and $y=b\sin \theta$ i.e., $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\left(a>b\right)$ is

$y=\frac{x^2}{1+x^2}$ divides the area enclosed by $y=\frac{1}{1+x^2},$ $x$-axis and $y$-axis in the first quadrant in the ratio

Area bounded by the parabola $y=x^2-2x+3$ and tangents drawn to it from the point $P\left(1,0\right)$ is equal to

Area in $\left(\mathrm{sq}. \mathrm{units}\right)$ bounded by the curve $y=\left(x-1\right)\left(x-2\right)\left(x-3\right)$, $x$-axis and ordinate $x=0, x=3$ is

The area of the region bounded by the curves $x^2+y^2=9$ and $x+y=3$ (in sq. units) is

A point $P$ moves in $xy$ plane in such a way that $\left[\left|x\right|\right]+\left[\left|y\right|\right]=1$, where $[.]$ denotes the greatest integer function. Area of the region representing all possible positions of the point $P$ is equal to

The area bounded by the circle $x^2+y^2=1$ and the curve $\left|x\right|+\left|y\right|=1$ is

What is the area of a loop of the curve $r=a\sin 3\theta$?