Vinod Singh and Shweta Pawar Solutions for Chapter: Applications of Definite Integral, Exercise 2: Critical Thinking

Area in $\left(\text{sq. units}\right)$ bounded by parabola $y^2=x$ and straight line $2y=x$ is

The area $\left(\text{in sq. units}\right)$ enclosed between the curves $y=x^3$ and  $y=\sqrt{x}$ is, (in square units)

The area enclosed by the parabolas $y=x^2-1$ and $y=1-x^2$  is

The area $\left(\text{in sq. units}\right)$ enclosed between the curves $y=x$ and $y=2x-x^2$ is (in square units)

Area bounded by the curve $x^2=4y$ and the straight line $x=4y-2$ is

If area in $\left(\text{sq. units}\right)$ bounded by the curves $y^2=4ax$ and $y=mx$  is $\frac{a^2}{3},$ then the value of $m$ is

The area in $\left(\text{sq. units}\right)$ bounded by the straight lines $x=0, x=2$ and the curves $y=2^x, y=2x-x^2$ is

Area of the region bounded by $\frac{x^2}{9}+\frac{y^2}{4}=1$ and the line $\frac{x}{3}+\frac{y}{2}=1$ is