Hello,
I have this question that I do not know how to do. If someone can solve this I will award points to the person who does. Thank you in advance.
Evaluate:
1. ∮c (ln x + y)dx - x^2 dy
where C is the rectangle with vertices (1, 1) (3, 1) (1, 4) and (3, 4).
Thanks,
-Rick
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Answers & Comments
Verified answer
Apply Green's Theorem:
∫c [(ln x + y)dx - x^2 dy]
= ∫∫ [(∂/∂x)(-x^2) - (∂/∂y)(ln x + y)] dA
= ∫(y = 1 to 4) ∫(x = 1 to 3) (-2x - 1) dy dx
= (4 - 1) * (-x^2 - x) {for x = 1 to 3}
= 3 * (-12 - (-2))
= -30.
I hope this helps!