# Two variable calculus

1. Feb 23, 2010

### Kate2010

1. The problem statement, all variables and given/known data

I have several problems:

1. Calculate $$\int\$$ F . dr over C
F = (y2,-x2) and C is the portion of the ellipse x2 + 4y2 = 4 which lies in the positive quadrant.

2. Calculate $$\int$$ (3x2 + 3y2)1/2 ds where C is the part of the hyperbola x2 - y2 = 1 from (1,0) to (cosh2, sinh2).

2. Relevant equations

3. The attempt at a solution

1. I have worked this out and got -20/3 but I'm unsure if it can be negative? I'm not very confident with working them out so am unsure about my answer. I can post more working if this is incorrect.

2. I assume I need to use the parameters x=cosht, y=sinht and integrate from 0 to 2. However, I am confused as to what I multiply by after I have subbed in for x=cosht and y=sinht, before I integrate, if that makes sense.

Last edited: Feb 23, 2010