Topic: Mathematics
The area bounded by the curves $y^{2}=x$, $y=x$ is given by
- A. $2/3$
- B. $1/2$
- C. $1/6$
- D. $1/3$
Answer: C. $1/6$
Explanation: $A=\int_{0}^{1}\int_{x}^{\sqrt{x}}dy dx=\int_{0}^{1}[y]_{x}^{\sqrt{x}}dx=\int_{0}^{1}[\sqrt{x}-x]dx=[\frac{2}{3}x^{3/2}-\frac{x^{2}}{2}]_{0}^{1}=\frac{2}{3}-\frac{1}{2}=\frac{1}{6}$.