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

$$calculate\int {\int }_C\mid x+y\mid dxdywithC=[-1,1]\times [-1,1]$$

Answered by ajfour last updated on 08/Dec/18

$$I=2{\int }_{-1}^1\left[{\int }_{-x}^1(x+y)dy\right]dx$$$$=2{\int }_{-1}^1(xy+\frac{y^2}{2}){\mid }_{-x}^{1}dx$$$$=2{\int }_{-1}^1(x+\frac{1}{2}+x^2-\frac{x^2}{2})dx$$$$=2{\int }_0^1(x^2+1)dx=\frac{8}{3}.$$

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

$$correctanswerthankssir.$$

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