Question

The area of the figure bounded by the parabola $x=-2y^2,x=1-3y^2$ is

• A. $\frac{1}{3}\text{square unit}$
• B. $\frac{4}{3}\text{square unit}$
• C. $1\text{square unit}$
• D. $2\text{square unit}$

Answer 1

The correct option is B $\frac{4}{3}\text{square unit}$


Required area
$=2\underset{0}{\overset{1}{\int }}(1-3y^2-(-2y^2\left)\right)dy$
$=2\underset{0}{\overset{1}{\int }}(1-y^2)dy$
$=2{[y-\frac{y^3}{3}]}_0^1$
$=\frac{4}{3}$