Question

The area enclosed by the curves $x^2=y,y=x+2$ and $x$-axis is:

• A. $\frac{5}{6}$
• B. $\frac{5}{4}$
• C. $\frac{5}{2}$
• D. $\frac{5}{3}$

Answer 1

Answer: (A)

$\frac{5}{6}$

$x^2=y,y=x+2$
$\left|\stackrel{-1}{\underset{-2}{\int }}\right(x+2\left)dx\right|+|\stackrel{0}{\underset{-1}{\int }}-x^{2}dx|$
$=\frac{x^2}{2}{|}_{-2}^{-1}+2\left(1\right)$
$=\frac{1}{2}-2+2+1/3=\frac{5}{6}squnits.$