Question

The area bounded by the parabola $x=y^2$ and the line $y=x-6$ is

• A. $\frac{125}{3}$ sq. units
• B. $\frac{125}{6}$ sq. units
• C. $\frac{125}{4}$ sq. units
• D. $\frac{115}{3}$ sq. units

Answer 1

Answer: (B)

$\frac{125}{6}$ sq. units

$x=y^2$ and the line $y=x-6$
area in $QI$+ area in QIV
$|\stackrel{3}{\underset{-2}{\int }}\left[\right(y+6)-y^2]dy|$
$=|{|\frac{y^2}{2}+6y-y^3/3|}_{-2}^3$
$=|\frac{9}{2}-\frac{4}{2}+6(5)-[\frac{27}{3}+8/3]|$
$|\frac{5}{2}+30-\left[\frac{35}{3}\right]|=\frac{15+180-70}{6}=\frac{125}{6}squnits.$