Calculating Drug Amount in a Capsule with Given Density Function and Dimensions

[DanBNyberg]

The question is asked in 3 parts. The first asks for the volume within the capsule.

The capsule has a radius=2mm total length=10mm, each end is rounded with r=2mm.
I have found the volume to be 108.9mm

The second part of the question gives a density function of the drug inside of the capsule.
It asks for the amount of drug inside of the capsule. The funtion is:

δ(x,y,z)=1/(6pi^2cosh5)* e^(-z)/root(4-x^2-y^2)

The capsule is oriented around the z axis, centered at the origin. Can you help me find what values to use for x,y,z,? Thanks!

 

[L-x]

This problem is probably easiest to approach using cylindrical polar co-ordinates. Try to remember how to convert x,y,x into r theta and z and the values to use should be obvious.

 

[DanBNyberg]

Is this where I chould head?
z=z
x=rcos theta
y=rsin theta

those substitutions into the denominator would give me:
root(4-(2cos theta)^2-(2sin theta)^2)
then:
root(4-4(cos^2 theta + sin^2 theta))
root(4-4(1))

I think I am off track again, I am getting root 0.

 

[L-x]

try again. Think integration rather than substituting in numbers.

Express r in terms of x and y, can you see that expression in the question?

 

[DanBNyberg]

Thanks for the help. So, I should integrate the function and convert to polar for the solution?