How Do I Set Up a Double Integral for a Cylinder's Volume in Polar Coordinates?

[whynot314]

Homework Statement

I want to convert this into polar and use double integral to find the volume of the solid in this region. I just need help setting this up
region
Q: x^2+y^2≤9, 0≤z≤4
I know this is a cylinder with a height of 4.
I am just having trouble incorporating this height into the integral.

The Attempt at a Solution

∫_0^2π▒〖∫_0^3▒4 r〗 drd(theta)
this is currently what I have

 

[whynot314]

"integral from 0 to 2pi" then integral 0 to 3. then 4 rdrdθ

 

[notorious_lx]

This is correct.
There is a cylinder with height 4. When using a double integral to find the volume of a solid object, you can set it up with the "Top - Bottom" as the function to integrate. This can also be done by adding in a third integral and integrating 1.
$\int_0^{2\pi} \int_0^3 \int_0^4 (1)dV$, where $dV$ is $rdzdrd\theta$.
$=\int_0^{2\pi} \int_0^3 (4) (r)drd\theta$
You can also check this by using the formula for the volume of a cylinder which is $\pi r^2h$

 

[whynot314]

thank you

 

[whynot314]

$\int^\3_\0$