Use Green's Theorem to evaluate the line integral along the given positively oriented curve. ∫C (3y +5e√x)dx + (10x + 3 cos y2)dy C is the boundary of the region enclosed by the parabolas y = x2 and x = y2

By Green's theorem, the line integral

is equivalent to the double integral

where D is the region bounded by the curve C, provided that this integrand has no singularities anywhere within D or on its boundary.

It's a bit difficult to make out what your integral should say, but I'd hazard a guess of

Then the region D is

D = {(x, y) : 0 ≤ x ≤ 1 and x ² ≤ y ≤ √x}

so the line integral is equal to

which in this case is 7 times the area of D.

The remaining integral is trivial:

answer: 38.47 is your answer

step-by-step explanation: hope i you and who ever sees this answer have a great rest of your day : )

i don't have the answer rn but go to math papa. it shows the steps and the answer. hope this : )

step-by-step explanation: