- #1
skrat
- 748
- 8
Homework Statement
Calculate the volume of a body given by plane ##z=0## and ##z=1## and ##x^2+y^2+z^2=4##.
Homework Equations
##detJ=r^2sin \theta## for spherical coordinates
The Attempt at a Solution
##V=\iiint_{T}^{}dV=\int_{0}^{2\pi }d\varphi \int_{0}^{1}dz\int_{\theta _{0}}^{\pi /2}r^2sin\theta d\theta ##
##V=\int_{0}^{2\pi }d\varphi \int_{0}^{1}dzr^2\frac{1}{2}##
##V=2\pi r^2\frac{1}{2}=\pi r^2=4\pi ##
Why is this wroooong? -.-
one more thing: trying to integrate by dx,dy and dz (having some troubles with integral borders):
##V=\int_{0}^{1}dz\int_{-2}^{2}dy\int_{-\sqrt{4-y^2-z^2}}^{\sqrt{4-y^2-z^2}}dx## or not?
Thanks for all the help!