Question

The area bounded by the curves $x=y^2$ and $x=3-2y^2$ is

• A. 2
• B. 4
• C. 4/3
• D. None of these

Answer 1

The correct option is B 4

As in the figure two curves represent parabolas with vertices at (0,0) and (3,0). They intersect at (1,1) and (1,-1), so the required area is
area of OPMQO= 2(area of OPMO ).



$=2\left({\int }_0^1\sqrt{x}dx+{\int }_1^3\sqrt{\frac{3-x}{2}}dx\right)=2(\frac{2}{3}{x}^{3/2}{|}_0^1-\frac{1}{\sqrt{2}}.\frac{2}{3}(3-x{)}^{3/2}{|}_1^3)=2[\frac{2}{3}-(0-\frac{1}{\sqrt{2}}.\frac{2}{3}{2}^{3/2})]=2(\frac{2}{3}+\frac{4}{3})=4$