Area of Solid/Convert to Cylindrical and Spherical

1. Nov 30, 2009

matt19weezy

1. The problem statement, all variables and given/known data
Convert to Cylindrical Coordinates from Cartesian

1st int(-2 to 2), 2nd int(-sqrt(4-x2) to sqrt (4-x2)), 3rd int((x2+y2) to 4) X dz dy dx.

I changed the integrals to Cylindrical 1st int(0 to pi), 2nd int(-2 to 2), 3rd int(r2 to 4) and the X to r cos(theta). r dz dr dtheta. I know this is wrong because I keep getting zero for the answer to area.

2. Relevant equations
Cylindrical- x=rcos(theta) y= r sin(theta) z=z

Cyl to Spherical- r= psin(fi) z=pcos(fi) fi=fi

3. The attempt at a solution
I changed the integrals to Cylindrical 1st int(0 to pi), 2nd int(-2 to 2), 3rd int(r2 to 4) and the X to r cos(theta). r dz dr dtheta. I know this is wrong because I keep getting sin(theta) and ending up with an area of 0.

2. Nov 30, 2009

LCKurtz

But you aren't calculating area. I suppose you meant you are calculating the volume and it can't be zero. But you aren't calculating volume either or the integrand would be 1 instead of x. In fact your integrand is antisymmetric in x (an odd function) so you would expect an answer of 0. In short, your work is correct. It's just your understanding of what you are calculating that is wrong.

3. Nov 30, 2009

matt19weezy

Wow. Duh. Thank you so much. I have been thinking this was incorrect the whole day. Of course now I see that I'm not solving for an area, I'm solving the integral. Oh thank you so much