Question

The area (in square units) of the region bounded by the curves $y+2x^2=0\text{and}y+3x^2=1$, is equal to :

• A. $\frac{1}{3}$
• B. $\frac{3}{4}$
• C. $\frac{3}{5}$
• D. $\frac{4}{3}$

Answer 1

The correct option is D $\frac{4}{3}$

The given equations are of parabola
$y+2x^2=0\text{and}y+3x^2=1$


So, the required area =$2\underset{0}{\overset{1}{\int }}\left[\right(1-3x^2)-(-2x^2\left)\right]dx=2\underset{0}{\overset{1}{\int }}(1-x^2)dx=2{[x-\frac{x^3}{3}]}_0^1=\frac{4}{3}\text{sq.units}$