Embibe Experts Solutions for Chapter: Area under Curves, Exercise 1: Exercise 1

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

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 of the region $\left\{\left(x, y\right):x^2+y^2\le 5, \Vert x|-|y\Vert \ge 1\right.\}$ is:

The area enclosed (in square units) by the curve $y=x^4-x^2,$ the $X$-axis and the vertical lines passing through the two minimum points of the curve is

Area bounded by the curve $x{y}^2=a^2\left(a-x\right)$ and $y$-axis is

Area of the region which consists of all the points satisfying the conditions $|x-y|+|x+y|\le 8$ and $xy\ge 2$ is equal to

The area of the closed figure bounded by $y=\frac{x^2}{2}-2x+2$ and the tangents to it at $\left(1,\frac{1}{2}\right)$ and $\left(4,2\right)$ is

Let $\text{'}c\text{'}$ be a positive real number such that area bounded by $y=0,y=\left[{\tan }^{-1}x\right]$ from $x=0$ to $x=c$ is equal to area bounded by $y=0, y=\left[{\cot }^{-1}x\right]$ from $x=0$ to $x=c$ (where $\left[*\right]$ represents greatest integer function), then