# Thread: Bounds for the triple integrals!

1. ## Bounds for the triple integrals!

Hello peeps!

I need help with setting up the integrals. I know how to evaluate but I need help setting it up!

1 ) The region common to the interiors of the cylinders x^2 + y^2 = 100 and x^2 + z^2 = 100. (cylindrical coordinates)

And also problems 14 (spherical coordinates), 18 (cylindrical coordinates) in the attachment.

please elaborate how you set up the integral on #14.

2. Originally Posted by aeubz
Hello peeps!

I need help with setting up the integrals. I know how to evaluate but I need help setting it up!

1 ) The region common to the interiors of the cylinders x^2 + y^2 = 100 and x^2 + z^2 = 100. (cylindrical coordinates)

And also problems 14 (spherical coordinates), 18 (cylindrical coordinates) in the attachment.

please elaborate how you set up the integral on #14.
#18 : By cylindrical coordinates:

$\displaystyle 0\leq z\leq r^2$

$\displaystyle 0\leq r\leq 10$

$\displaystyle 0\leq\vartheta\leq 2\pi$

So, your integral is $\displaystyle \int_0^{2\pi}\int_0^{10}\int_0^{r^2}r\,dz\,dr\,d\v artheta$

I'm sure you capable of solving this...

--Chris