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

The value of the parameter $\text{'}a\text{'}$ such that the area bounded by $y=a^2{x}^2+ax+1,$ coordinate axes and the line $x=1$ attains its least value, is equal to

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

If area enclosed by the curves $y=x \ln x$ and $y=2x(1-x)$ is $A$, then $\left[A\right]$ equals, where $\left[*\right]$ denotes greatest integer function.

The area inside the parabola $5x^2-y=0$ but outside the parabola $2x^2-y+9=0$ is

The area bounded by the curves $y=x{e}^x, y=x{e}^{-x}$ and the line $x=1$ (in sq. units) is

What is the area of the region bounded by the parabolas $y^2=6(x-1)$ and $y^2=3x$?