Question

Integrate h(x, y) = (x + y) i + (y2 - x) j over the closed curve that begins at (-7, 0), goes along the x-axis to (7, 0) and returns to (-7, 0) by the upper part of the circle x2 + y2 = 49

Answer 1

Integrate h(x, y) = (x + y) i + (y^2 - x) j over the closed curve that begins at (-7, 0), goes along the x-axis to (7, 0) and returns to (-7, 0) by the upper part of the circle x^2 + y^2 = 49

Answer 2

(This is using greens theorum)

Answer 3

P = x+y
Py = 1

Q = y^2-x
Qx = -1

\[\large\rm \oint_c (x+y)dx+(y^2-x)dy\quad=\quad \int\limits\int\limits_D-1-1~dA\]We get something like that, yes?

Are you having trouble with the boundaries?