# Show F(x,y)=(2xy3+8)i+(3x2y2+2e2y)j is conservative by finding a potential function f for F, and use f to compute ∫CF⋅dr, where C is the...?

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• rotchm
Lv 7
4 weeks ago

Find a scalar function f(x,y) such that ∂f/∂x = 2xy3+8 and

∂f/∂y = 3x2y2+2e2y. This requires but integrations, which you know how to do. So, what f(x,y) have you found?

Since you found one, then F is conservative.

Now, knowing that F is conservative, you can evaluate any line integral by just using the potential function f(x,y) you found. Whats the procedure? What do you get?