A) \[\frac{1}{9}\]
B) \[\frac{1}{3}\]
C) \[\frac{1}{\sqrt{3}}\]
D) \[\frac{2}{3}\]
Correct Answer: B
Solution :
Solving, y = x2 and x = y2 \[y={{y}^{4}}\]or \[y({{y}^{3}}-1)=0\Rightarrow y=0\]or y = 1 \[\therefore \]Point of intersection are (0,0) &(1,1) To find the shaded area, \[A=\int_{0}^{1}{(\sqrt{x}-{{x}^{2}})dx}\] \[=\frac{2}{3}\left[ {{x}^{3/2}} \right]_{0}^{1}-\left[ \frac{{{x}^{3}}}{3} \right]_{0}^{1}=\frac{2}{3}-\frac{1}{3}=\frac{1}{3}\]You need to login to perform this action.
You will be redirected in
3 sec