Calculus 3!!!!! Evaluate the line integral ∫xe^(4x) dx-6x^3 ydy along a closed rectangle.

Evaluate the line integral ∫xe^(4x) dx-6x^3 ydy along a closed rectangle from (0,0) to (6,0) to (6,4) to (0,4).

Please provide the correct answer with the worked out solution.
Thank you in advance. Your help is greatly appreciated!! The best answer will be chosen.

Since the path is closed, we can use Green's Theorem.
∫c [xe^(4x) dx - 6x^3y dy]
= ∫∫ [(∂/∂x) (-6x^3y) - (∂/∂y) (xe^(4x))] dA
= ∫(x = 0 to 6) ∫(y = 0 to 4) -12x^2y dy dx
= ∫(x = 0 to 6) -6x^2 dx * ∫(y = 0 to 4) 2y dy
= [-2x^3 {for x = 0 to 6}] * [y^2 {for y = 0 to 4}]
= -432 * 16
= -6912.

I hope this helps!