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Question Number 44424 by peter frank last updated on 28/Sep/18

b y c o n s i d e r i n g a s e r m i c i r c l e f r o m - r t o r p r o v e t h a t a r e a o f c i r c l e i s π r^{2}

Answered by tanmay.chaudhury50@gmail.com last updated on 29/Sep/18

2 \int_{- r}^{r} \sqrt{r^{2} - x^{2}} d x

2 \times ∣ \frac{x \sqrt{r^{2} - x^{2}}}{2} + \frac{r^{2}}{2} {s i n}^{- 1} (\frac{x}{r}) ∣_{- r}^{r}

= 2 \times \frac{r^{2}}{2} {{s i n}^{- 1} (\frac{r}{r}) - {s i n}^{- 1} (\frac{- r}{r})}

= r^{2} {\frac{π}{2} - (- \frac{π}{2})}

= r^{2} \times π

a r e a o f c i r c l e o f r a d i u s r = π r^{2}

Commented by peter frank last updated on 29/Sep/18

w h e r e t h i s c a m e f r o m \sqrt{r^{2} - x^{2} ?}

Commented by tanmay.chaudhury50@gmail.com last updated on 29/Sep/18

e q n o f c i r c l e x^{2} + y^{2} = r^{2}

y = \sqrt{r^{2} - x^{2}}

Commented by peter frank last updated on 29/Sep/18

o k a y s i r t h a n k y o u