Multivariable Calculus

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Moderate

Find Potential Function from Gradient

MVCALC-1LMW4K

If $\phi(x,y)$ is a potential function for the gradient vector field:

$$\vec{F}=\langle 2xy-4\cos y, x^2 +4x\sin y\rangle$$

...evaluate:

$$\phi(2,\frac{\pi}{2})-\phi(1,0)$$

A

$\pi+4$

B

$2\pi+4$

C

$2\pi+8$

D

$\vec{F}$ is not a gradient field

E

Not enough information to determine