Area of Solid/Convert to Cylindrical and Spherical

[matt19weezy]

Homework Statement

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.

Homework Equations

Cylindrical- x=rcos(theta) y= r sin(theta) z=z

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

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