A) \[9\pi \]
B) \[4\pi \]
C) \[36\pi \]
D) \[6\pi \]
Correct Answer: D
Solution :
The given equation of curve is \[9{{x}^{2}}+4{{y}^{2}}-36\] or it can written as \[\frac{{{x}^{2}}}{4}+\frac{{{y}^{2}}}{9}=1\] Required area = Area of curve ADCBA = 4 Area of curve OCBA \[=4\int_{0}^{3}{3\sqrt{1-\frac{{{x}^{2}}}{4}}\,dx=6}\,\int_{0}^{2}{\sqrt{4-{{x}^{2}}}\,dx}\] \[=6\,\left[ \frac{x}{2}\sqrt{4-{{x}^{2}}}+\frac{4}{2}{{\sin }^{-1}}\frac{x}{2} \right]_{0}^{2}\] \[=6\,\left[ 0+2{{\sin }^{-1}}1-(0+2\,(0)) \right]\] \[=6\,\,.\,\,2\,.\frac{\pi }{2}=6\,\pi \]You need to login to perform this action.
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