A) 9 sq unit
B) \[\frac{27}{4}\] sq unit
C) 36 sq unit
D) 18 sq unit
Correct Answer: A
Solution :
Required area of shaded portion OABO \[=\int_{0}^{9}{\sqrt{x}}dx-\int_{3}^{9}{\left( \frac{x-3}{2} \right)dx}\] \[=\left[ \frac{{{x}^{3/2}}}{3/2} \right]_{0}^{9}-\frac{1}{2}\left[ \frac{{{x}^{2}}}{2}-3x \right]_{3}^{9}\] \[=\left( \frac{2}{3}.27 \right)-\frac{1}{2}\left[ \left( \frac{81}{2}-27 \right)-\left( \frac{9}{2}-9 \right) \right]\] \[=18-\frac{1}{2}(18)=9\]sq unitYou need to login to perform this action.
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