Question

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

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{4}{3}$
• D. $\frac{8}{3}$

Answer 1

Answer: (B)

$\frac{2}{3}$

$\begin{array}{c}{\int }_{-1}^1(y_2-y_1)dx\\ ={\int }_{-1}^1{x}^2-1-(1-x^2)dx\\ ={\int }_{-1}^{1}2x^2-2x^{}dx\\ ={[\frac{2x^3}{3}-2x]}_{-1}^1\end{array}$

$\begin{array}{c}=\frac{2}{3}-2-[\frac{-2}{3}+2]\\ =\frac{4}{3}\end{array}$