Use-polar-co-ordinates-to-evaluate-R-e-x-2-y-2-dA-where-the-region-R-is-enclosed-by-the-circle-x-2-y-2-1-

Question Number 26601 by 01779506249 last updated on 27/Dec/17

U s e p o l a r c o - o r d i n a t e s t o e v a l u a t e \int \int_{R} e^{- (x^{2} + y^{2})} d A, w h e r e t h e r e g i o n R i s e n c l o s e d b y t h e c i r c l e x^{2} + y^{2} = 1 .

Answered by ajfour last updated on 27/Dec/17

= \int_{0}^{2 π} \int_{0}^{1} e^{- r^{2}} (r d r) d θ

= π \int_{1}^{0} e^{- r^{2}} (- 2 r d r) = π (e^{- r^{2}}) ∣_{1}^{0}

= π (1 - \frac{1}{e}) .

Facebook Tweet Pin