calculate-C-x-y-dxdy-with-C-1-1-1-1-

Question Number 49645 by maxmathsup by imad last updated on 08/Dec/18

c a l c u l a t e \int \int_{C} ∣ x + y ∣ d x d y w i t h C = [- 1, 1] \times [- 1, 1]

Answered by ajfour last updated on 08/Dec/18

I = 2 \int_{- 1}^{1} [\int_{- x}^{1} (x + y) d y] d x

= 2 \int_{- 1}^{1} (x y + \frac{y^{2}}{2}) ∣_{- x}^{1} d x

= 2 \int_{- 1}^{1} (x + \frac{1}{2} + x^{2} - \frac{x^{2}}{2}) d x

= 2 \int_{0}^{1} (x^{2} + 1) d x = \frac{8}{3} .

Commented by maxmathsup by imad last updated on 09/Dec/18

c o r r e c t a n s w e r t h a n k s s i r .