Do not need help with the first two. I need help with the last questoin pertaini

Question

Do not need help with the first two. I need help with the last questoin pertaining to outer path and Green's theorem.

Consider the planar vector field Pi Qj with Show that Oy Continuing the previous problem, evaluate the line integral Jr P dz ay, where is the circle r y 1 in the counter-clockwise sense, by parametrizing the circle. Explain why an application of Green's theorem would not be valid. Continuing the previous problem, use the result of the previous problem and Green's theorem to evaluate JT, Pdar Q dy where I'1 is the outer path in this figure (1,0) (0,0)

Explanation / Answer

Now, you say you do not need help on the first two, thats fine.

For the last part, we still need the equation of the outer loop, but theres no problem there because.....

No matter what the figure is, since dQ/dx and dP/dy were the same,

by greens theorem which says that

(line integral) Pdx + Qdy = (double integral) dQ/dx - dP/dy * dA

---> (line integral) Pdx + Qdy = (double integral) 0 * dA

----> (line integral) Pdx + Qdy = (double integral) = 0

So, the answer is

ZERO -----> ANSWER

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