Question

The area enclosed by the curves $3x^2+5y=32$ and $y=|x-2|$ is

• A. $\frac{13}{2}$ sq. units
• B. $\frac{17}{2}$ sq. units
• C. $\frac{23}{2}$ sq. units
• D. $\frac{33}{2}$ sq. units

Answer 1

Answer: (D)

Given that $3x^2+5y=32$, a parabola with vertex $\left(0,6.4\right)$.

$A={\int }_{-2}^3\frac{32-3x^2}{5}dx-\frac{4\times 4}{2}-\frac{1\times 1}{2}$
$=32-\frac{1}{5}\left(27+8\right)-\frac{17}{2}$
$=25-\frac{17}{2}$
$=\frac{33}{2}$ sq. units