Definite Integration Question 289
Question: The area bounded by the curves $ y^{2}=8x $ and $ y=x $ is
Options:
A) $ \frac{128}{3} $ sq. unit
B) $ \frac{32}{3} $ sq. unit
C) $ \frac{64}{3} $ sq. unit
D) 32 sq. unit
Show Answer
Answer:
Correct Answer: B
Solution:
$ y^{2}=8x $ and $ y=x\Rightarrow x^{2}=8x\Rightarrow x=0 $ ,8 Required area = $ \int_0^{8}{(2\sqrt{2}\sqrt{x}-x)dx} $
$ =[ \frac{4\sqrt{2}}{3}{x^{3/2}}-\frac{x^{2}}{2} ]_0^{8}=\frac{128}{3}-\frac{64}{2}=\frac{32}{3}sq. $ unit.
BETA
