Definite Integration Question 178
Question: The figure shows as triangle AOB and the parabola $ y=x^{2} $ . The ratio of the area of the triangle AOB to the area of the region AOB of the parabola $ y=x^{2} $ is equal to
Options:
A) $ \frac{3}{5} $
B) $ \frac{3}{4} $
C) $ \frac{7}{8} $
D) $ \frac{5}{6} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Area of $ \Delta AOB=\frac{1}{2}\times 2a\times a^{2}=a^{3} $ units
Area of region AOB $ =2\int\limits_0^{a^{2}}{xdy=2\int\limits_0^{a^{2}}{\sqrt{y}dy=2[ \frac{{y^{3/2}}}{3/2} ]_0^{a^{2}}=\frac{4}{3}a^{3}}} $ units
$ \therefore $ ratio of areas $ =\frac{a^{3}}{\frac{4}{3}a^{3}}=\frac{3}{4} $
BETA
