Finding the Volume of Two Solids: A Cylindrical Approach

[tifa8]

Hello I need help for this problem, it has been 4 hours trying to do it

Homework Statement

Find the volume of the region of space above the xy-plane, inside the cone z=7−$$\sqrt{x^{2}+y^{2}}$$ and inside the cylinder x$$^{2}$$+y$$^{2}$$=4x.

Homework Equations

The Attempt at a Solution

I tried to switch to cylindrical coordinates and I got

0$$\leq$$$$\theta$$$$\leq$$2$$\pi$$
0$$\leq$$r$$\leq$$4cos($$\theta$$)
0$$\leq$$z$$\leq$$7-r

so,
V=$$\int^{2\pi}_{0}\int^{4cos(\theta)}_{0}\int^{7-r}_{0}$$rdzdrd$$\theta$$
which doesn't work...

thanks in advance

 

[SammyS]

I think you'll find that θ goes from -π/2 to π/2 .

 

[tifa8]

thank you

 

[lramsa1]

I think you'll find that θ goes from -π/2 to π/2 .

How did you find these bounds?