1. ## Conservative field

Confirm that $\displaystyle F$ is conservative and calculate the work realized y field of forces a particle that moves of $\displaystyle P$ to $\displaystyle Q$ along of one curve arbitrary in region of $\displaystyle P$ to $\displaystyle Q$.

$\displaystyle F(x,y) = 2xy^3 i + 3x^2y^2 j$
$\displaystyle P(-3,0); Q(4,1)$

Solution

deriving:
$\displaystyle 6xy^2 = 6xy^2$ is conservative

How do I calculate the work?

2. If F is a force field theline integral is the work

For an explanation of why see my website Line Integrals

3. ok, line integral = work

$\displaystyle W = 6xy^2 |_{(-3,0)}^{(4,1)} = 24$

Is correct ?

4. Not quite you're potential function is x^2y^3

5. $\displaystyle W = x^2y^3 |_{(-3,0)}^{(4,1)} = 16$

New is correct ?

6. Yes---okay you know how to do this --in earlier posts

you learned how to find the potential function --slown down and put it all together

7. Originally Posted by Calculus26
Yes---okay you know how to do this --in earlier posts

you learned how to find the potential function --slown down and put it all together
yes thank you