prove-by-useing-the-polar-cordinaite-0-a-2-y-a-2-y-2-x-dx-dy-5-a-3-24-

Question Number 167576 by mkam last updated on 19/Mar/22

p r o v e b y u s e i n g t h e p o l a r c o r d i n a i t e

\int_{0}^{\frac{a}{2}} \int_{y}^{\sqrt{a^{2} - y^{2}}} x d x d y = \frac{5 a^{3}}{24}

Commented by mkam last updated on 20/Mar/22

? ? ? ? ?

Answered by ArielVyny last updated on 19/Mar/22

\int_{0}^{\frac{a}{2}} {[\frac{1}{2} x^{2}]}_{y}^{\sqrt{a^{2} - y^{2}}} d y = \int_{0}^{\frac{a}{2}} \frac{1}{2} a^{2} - y^{2}

= \frac{1}{2} a^{2} [\frac{a}{2}] - \frac{1}{3} [\frac{a^{3}}{8}] = \frac{6 a^{3}}{24} - \frac{a^{3}}{24} = \frac{5 a^{3}}{24}

Commented by ArielVyny last updated on 19/Mar/22

w h y u s i n g p o l a r c o o r d i n a t e s

Commented by mkam last updated on 19/Mar/22

b e c a u s e m y t e a c h e r w a n t e d t h i s m e t h o d

Commented by JDamian last updated on 19/Mar/22

Oh, what kind of you for doing his homework