## Trending News

Promoted

# Work done by a radial force field???

Let F be the radial force field F = xI + yJ. Find the work done by this force along the following two curves, both which go from (0, 0) to (8, 64). (Use the Fundamental Theorem for Line Integrals instead of computing the line integral from the definition)

A. If C1 is the parabola: x = t, y = t^2, 0 ≤ t ≤ 8, then ∫C1 F · dX =

B. If C2 is the straight line segment: x = 8 t^2, y = 64 t^2, 0 ≤ t ≤ 1, then ∫C2 F · dX =

### 1 Answer

Relevance

- kbLv 79 years agoFavorite Answer
Note that ∇(x^2/2 + y^2/2) = <x, y>; so the Fundamental Theorem for Line Integrals applies.

For both (a) and (b):

t = 0 ==> (x, y) = (0, 0), and t = 8 ==> (x, y) = (8, 64).

Therefore, ∫c F · dX = (x^2/2 + y^2/2) {for (x, y) = (0, 0) to (8, 64)} = 2080.

I hope this helps!

Still have questions? Get your answers by asking now.