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How would you use Green's Theorem to compute the integral below?
Using Green's Theorem to compute
∫ x^2y^3 dx- xy^2 dy
C
where C is the boundary of the square centered at the origin and with vertices (3/4, 3/4), (-3/4, 3/4), (-3/4, -3/4), and (3/4, -3/4) and the closed path is oriented counterclockwise.
a. -17/3072
b. -5/48
c. -675/1024
d. -8/3
e. -351/16
f. -320/3
g. -18,125/48
h. -1080
i. -37,375/96
or is it none of these ?
1 Answer
- Sean HLv 51 decade agoFavorite Answer
Use Green's theorem to change it to an integral over the interior of the square. Since the boundary is oriented counterclockwise you get:
∫ x^2y^3 dx- xy^2 dy
C
=
∫ ∫ (-3x^2 y^2 - y^2) dx dy
S
where S is the square. Now apply Fubini's theorem to turn the 2-d integral into an interated integral and evaluate that.
