- #1
Calpalned
- 297
- 6
Homework Statement
Use Green's Theorem to evaluate the line integral along the given positively oriented curve.
1) Is the statement above the same as finding the area enclosed?
2) ##\int_C \cos ydx + x^2\sin ydy ##, C is the rectangle with vertices (0,0) (5,0) (5,2) and (0,2).
3) ##\int_C y^4 dx + 2xy^3dy ##, C is the ellipse ##x^2 + xy^2 = 2##
4) ## \int_C {(1-y^3)dx + (x^3+e^\psi)dy} ##, where ##\psi = y^2## and C is the boundary of the region between the circles ##x^2 + y^2 =4## and ##x^2 + y^2 =9##
Homework Equations
n/a
The Attempt at a Solution
I solved all of these questions, with the exception of the first one. Unfortunately, these do not come with answers, so I would like to check if my answers are correct. For questions 2 to 3, I just wrote out Green's double integral.
1) Yes
2) ##\int_0^2 \int_0^5 (\sin y(2x+1)) dxdy ##
3) ##\int \int -2\sin ^3 \theta d \theta ##
4) ##\int_0^{2\pi} \int_2^3 3r^3 drd \theta ##
I think I got #1 and #3 wrong. If they are wrong, I will put up my original solution attempt. .
Note to self: Stewart, page 1090, 1 refers to question 6, 2 = 8 and 3 = 10.
Thanks everyone!
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