- #1
tifa8
- 14
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Hello I need help for this problem, it has been 4 hours trying to do it
Find the volume of the region of space above the xy-plane, inside the cone z=7−[tex]\sqrt{x^{2}+y^{2}} [/tex] and inside the cylinder x[tex]^{2}[/tex]+y[tex]^{2}[/tex]=4x.
I tried to switch to cylindrical coordinates and I got
0[tex]\leq[/tex][tex]\theta[/tex][tex]\leq[/tex]2[tex]\pi[/tex]
0[tex]\leq[/tex]r[tex]\leq[/tex]4cos([tex]\theta[/tex])
0[tex]\leq[/tex]z[tex]\leq[/tex]7-r
so,
V=[tex]\int^{2\pi}_{0}\int^{4cos(\theta)}_{0}\int^{7-r}_{0}[/tex]rdzdrd[tex]\theta[/tex]
which doesn't work...
thanks in advance
Homework Statement
Find the volume of the region of space above the xy-plane, inside the cone z=7−[tex]\sqrt{x^{2}+y^{2}} [/tex] and inside the cylinder x[tex]^{2}[/tex]+y[tex]^{2}[/tex]=4x.
Homework Equations
The Attempt at a Solution
I tried to switch to cylindrical coordinates and I got
0[tex]\leq[/tex][tex]\theta[/tex][tex]\leq[/tex]2[tex]\pi[/tex]
0[tex]\leq[/tex]r[tex]\leq[/tex]4cos([tex]\theta[/tex])
0[tex]\leq[/tex]z[tex]\leq[/tex]7-r
so,
V=[tex]\int^{2\pi}_{0}\int^{4cos(\theta)}_{0}\int^{7-r}_{0}[/tex]rdzdrd[tex]\theta[/tex]
which doesn't work...
thanks in advance