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## Homework Statement

show that F is path independant. Then evaluate the integral F dot dr on c, where c = r(t) = (t+sin(pi)t) i + (2t + cos(pi)t) j, 0<=t<=1

## Homework Equations

## The Attempt at a Solution

F = 4x^3y^2 + 2xy^3 i + 2x^4y - 3x^2y^2 + 4y^3 j

grad f = 12x^2y^2 + 2y^3 i + 2x^4 - 6x^2y + 12y^2 j not sure i need this

my instructor talked about numerouse way to determine path independace. which is the easiest