Find-the-area-common-to-the-curve-y-2-12x-and-x-2-y-2-24x-

Question Number 140615 by bramlexs22 last updated on 10/May/21

Find the area common

to the curve y^{2} = 12 x and

x^{2} + y^{2} = 24 x .

Answered by EDWIN88 last updated on 10/May/21

Area = \frac{2}{3} . 24.12^{4} + \frac{π}{2} . 144^{72}

= 192 + 72 π

Commented by EDWIN88 last updated on 10/May/21

Commented by Dwaipayan Shikari last updated on 10/May/21

\int_{0}^{12} \sqrt{12 x} d x = \frac{2 \sqrt{12}}{3} (12 \sqrt{12}) = 96 (H a l f p a r t i n p o s i t i v e h a l f)

x^{2} - 24 x + y^{2} = 0 \Rightarrow {(x - 12)}^{2} + y^{2} = 12^{2}

O t h e r h a l f = \frac{π}{4} {(12)}^{2} = 36 π

T o t a l A r e a i n e n c l o s e d i n t w o h a l v e s = 2 (96 + 36 π) = 192 + 72 π