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

Find the area of the region bounded by $y=\left\{x\right\}$ and $2x-1=0, y=0$ ($\left\{·\right\}$ stands for fractional part)

Find the area included between the parabolas $y^2=x$ and $x=3-2y^2.$

A tangent is drawn to the curve $x^2+2x-4ky+3=0$ at a point whose abscissa is $3$. This tangent is perpendicular to $x+3=2y.$ Find the area bounded by the curve, this tangent and ordinate $x=-1$

If $A_n$ is the area bounded by the curve $y={\left(\tan x\right)}^n$ and the lines $x=0, y=0$ and $x=\frac{\pi }{4}$. Then, prove that for $n>2$, $A_n+A_{n+2}=\frac{1}{n+1}$ and deduce $\frac{1}{2n+2}<A_n<\frac{1}{2n-2}$.

The area of the figure bounded by right of the line $y=x+1, y=\cos x$ and $x$-axis is

Area bounded by curve $y^3-9y+x=0$ and $y$-axis is

The area bounded by $y=2-\left|2-x\right|$ and $y=\frac{3}{\left|x\right|}$ is