Use cylindrical coordinates to calculate the triple integral [ f(x, y, z) dV for the function f(x, y, z) = 2704 ²√x² + y² and the region x² + y² ≤ z≤ 52 - (x² + y²). (Express numbers in exact form. Use symbolic notation and fractions where needed.) W f(x, y, z) dV =

solve. Show all the step.

Apply Green's Theorem to evaluate the integral. f4y+ +x) dx + (y + 5x)dy C: The circle (x − 4)² + (y − 8)² <= 4

b) Calculate the line integral of F along the boundary of the rectangle [0, 1 x[-1, 2], traversed once in the clockwise direction.