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## Homework Statement

F = (3x

^{2}+ 2y cos(xy))i + (2y + 2x cos(xy))j

a - show that F is a gradient field

b - calculate the integral of F dot dr where c includes the points -2,0 and 2,0

c - determine the value of the integral of F dot dr where c is any curve joining -2,0 and 2,0

## Homework Equations

## The Attempt at a Solution

a..

grad f = F,

I found f = x

^{3}+ y

^{2}- 2sin(xy)

b.....

curlf F = 0, therefore the integral F dot dr = curl F dot dA = 0

c.......

wouldnt that be the same as the above b