Evaluate Integral

Question

Evaluate Integral_C F * dr, where F(x,y) = (6x-2y)i +x^(2)j, and C is the line segment from (6,-3) to (0,0).

Thanks in advance!

Answer 1

Slope m = (0 + 3)/(0 - 6) = - 1/2; y =- x/2, and x changed from 6 to 0.

∫_CF•dr = ∫_C[(6x - 2y)dx + x²dy] = ∫₆⁰[(6x + x)dx -1/2x²dx] = ∫₆⁰(7x - 1/2x²)dx = (7x²/2 - x³/6)₆⁰ = - 90