A) \[\frac{8{{a}^{2}}}{3}sq\,\,unit\]
B) \[\frac{16{{a}^{2}}}{3}sq\,\,unit\]
C) \[\frac{32{{a}^{2}}}{3}sq\,\,unit\]
D) \[\frac{64{{a}^{2}}}{3}sq\,\,unit\]
Correct Answer: B
Solution :
Given equation of curves are \[{{y}^{2}}=4ax\]and\[{{x}^{2}}=4ay\] The point of intersection of above curves are\[(0,\,\,0)\]and\[(4a,\,\,4a)\]. \[\therefore \]Required area \[=\] Area of shaded curve \[=\int_{a}^{4a}{\left( \sqrt{4ax}-\frac{{{x}^{2}}}{4a} \right)dx}\] \[=\left[ \sqrt{4a}\frac{{{x}^{3/2}}}{3/2}-\frac{{{x}^{2}}}{12a} \right]_{0}^{4a}\] \[=\frac{32{{a}^{2}}}{3}-\frac{16{{a}^{2}}}{3}\] \[=\frac{16{{a}^{2}}}{2}sq\,\,unit\]You need to login to perform this action.
You will be redirected in
3 sec