Question

Find the area of the region bounded by the curve $y=x^2$ and the line $y=4$.

Answer 1

Let the area bounded by the curves $y=x^2$ and $y=4$ be $A$

The line $y=4$ cuts the curve $y=x^2$ at $x=\pm 2$

The area of rectangle formed by points $(2,0),(-2,0),(2,4),(-2,4)$ is $4\times 4=16$

The area made by curve $y=x^2$ with $x$ axis in the region $-2<x<2$ is $2{\int }_{-2}^2{x}^2=\frac{16}{3}$

Therefore the required area $A=16-\frac{16}{3}=\frac{32}{3}$