Area of Solid/Convert to Cylindrical and Spherical

[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.

[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.

[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