1. ## Line integral of grad(f).

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. $$\int_C\vec{F}\cdot d\vec r =$$$

2. Why is the gradient not a vector? Find the vector form and have at it!

3. I think I might of figured this one out:

$\displaystyle \int_{C}^{}F*dr=f(0,2)-f(2,0)$
$\displaystyle =(2(0)^2+5(2)^3)-(2(2)^2+5(0)^3)$
$\displaystyle 32$

4. Originally Posted by Zanderist
I think I might of figured this one out:

$\displaystyle \int_{C}^{}F*dr=f(0,2)-f(2,0)$
$\displaystyle =(2(0)^2+5(2)^3)-(2(2)^2+5(0)^3)$
$\displaystyle 32$
Correct.