Embibe Experts Solutions for Chapter: Area under Curves, Exercise 2: Level 2

The area of the region bounded by $x=0, y=0, x=2, y=2, y\le e^x$ and $y\ge \ln x$ is

The area bounded by the curves $y=x{e}^x, y=x{e}^{-x}$ and the line $x=1$ is

Area enclosed between the curves $\left|y\right|=1-x^2$ and $x^2+y^2=1$ 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

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

The area of the region bounded by the curves $y=ex{\log }_{e}x$ and $y=\frac{{\log }_{e}x}{ex}$ is

If the area bounded by the curves $y=3-\left|3-2x\right|$ and $y=\frac{5}{\left|2x\right|}$ is $A$ when $x<\frac{3}{2}$, then $\left[A\right]$ equals where $\left[*\right]$ denotes greatest integer function.

If the area bounded by $y=f^{-1}\left(x\right), x=10, x=4$ and $x$-axis given that area bounded by $y=f\left(x\right), x=2, x=6$ and $x$-axis is $30 \mathrm{sq}.\mathrm{units}$, where $f\left(2\right)=4$ and $f\left(6\right)=10$ is $k$ sq. units, then the value of $k$ is,

 (given $f\left(x\right)$ is an invertible function)