Let be the positively oriented square with vertices (0,0)(0,0), (2,0)(2,0), (2,2)(2,2), (0,2)(0,2). use green's theorem to evaluate the line integral ∫+∫c10y2xdx+4x2ydy.

-48

Step-by-step explanation:

Lets call L(x,y) = 10y²x, M(x,y) = 4x²y. Green's Theorem stays that the line integral over C can be calculed by computing the double integral over the inner square  of Mx - Ly. In other words

Where Mx and Ly are the partial derivates of M and L with respect to the x variable and the y variable respectively. In other words, Mx is obtained from M by derivating over the variable x treating y as constant, and Ly is obtaining derivating L over y by treateing x as constant. Hence,

Therefore, the line integral can be computed as follows

Using the linearity of the integral and Barrow's Theorem we have

As a result, the value of the double integral is -48-

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step-by-step explanation: