' Suppose that f(x, y) = e³/ on the domain D = {(x, y) | 0 ≤ y ≤ 2,0 ≤ x ≤ y³}. D Then the double integral of f(x, y) over D is [ [ f(x, y)dxdy =

Compute the real part of the integral [ Answer: f(z)dz where f(z) = u(x, y) + iv(x, y) with u(x, y) = x + y²,v(x, y) = y + x² and contour C is the straight line z(t) = (5.5-8.2i)r with t E (0, 1).

Calculate the line integral f(3xy³ − 4x + 4y + 8) dx + (−3xy+5) dy, where C' is the rectangle with vertices (2, −4), (2, -3), (−3,−3), and (−3,-4) oriented clockwise. Enter an exact answer. Provide your answer below: f(3x³ 4x + 4y + 8) dx + (−3xy + 5) dy =