# Question: Line Integrals

April 01 2010 by
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Let F(x, y) = 4x + 5ye i + 5y cos y + 5xe j.

> P := (x, y)− > 4 ∗ x^2 + 5 ∗ y ∗ exp(x ∗ y);

> Q := (x, y)− > 5 ∗ y ∗ cos(y) + 5 ∗ x ∗ exp(x ∗ y);

> diff(Q(x, y), x) − diff(P(x, y), y);

Is the vector field F conservative? (YES or NO)

Using the above or otherwise, write down a potential function f of F. (Enter an expression of f in terms of x and y)