Question

The area bounded by the parabola $x=4-y^2$ and the $Y$-axis, in square units is

• A. $\frac{3}{32}$
• B. $\frac{32}{3}$
• C. $\frac{33}{2}$
• D. $4$

Answer 1

Answer: (B)

$\frac{32}{3}$

$x=4-y^2$ and the $Y$-axis
$y^2=4-x$
$y=\sqrt{4-x}$
Area of shaded region=$\left|2\stackrel{4}{\underset{0}{\int }}\sqrt{4-x}dx\right|$
$=|-2(4-x{)}^{3/2}\times 2/3{|}_0^4$

$=2(4{)}^{3/2}\times 2/3$

$=\frac{32}{3}squnits$