I really don't know where to begin on this one since all of my notes give me a vector; This looks like I'm given a gradient and I do not know what I need to do to start this.

I do know however, that I will have to parametrize with spherical coordinates.

But I do not know what theorem this is.

$\displaystyle If \(\vec F=\nabla (2x^{2}+5y^{3})\),$

$\displaystyle find \(\int_C\vec{F}\cdot d\vec r\) where \(C\) is the quarter of the circle \(x^2+y^2 = 4\) in the first quadrant, $

$\displaystyle oriented counterclockwise.

\(\int_C\vec{F}\cdot d\vec r =\)$