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4. Use the theorem of Green to evaluate the integral lines.b. ∮_c y^2 dx+xydy, C: boundary of the region to understand and

4\. Use the theorem of Green to evaluate the integral lines.b. ∮\_c y^2 dx+xydy, C: border of the region between the graphs y=0 and the curve y=x^(1/2) and x=9 How it develops

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;) Hi jennifer ! From the mobile I can not open the Equation Editor! The region is a closed curve of vertices (0,0), (9,0), (9,3), then the integral in line can be calculated as an integral (Int) I turned in that precinct {R}, by applying the Theorem of Green: Int Int (Q\_x-P\_y)dxdy P=y^2 Q=xy partial derivative with respect to x : Q\_x=y partial derivative with respect to and: P\_y=2y We integrate twice, the limits are in brackets: Int\[0,3\] Int\[y^2,9\] (y-2y) dx dy= Int\[0,3\] Int\[y^2,9\] (-y) dx dy= -Int\[0,3\] yx. |\[y^2,9\]dy= -Int\[0,3\] and(9-y^2) dy = -Int \[0,3\] (9y-y^3) dy = \- (3y^2 - y^4/4). \[0.3\]= -(27 - 81/4)= -6.75

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