integration of the variables? Okay so i know how to convert rectangle coordinates into cylindrical coordinates easily, I just get confused when you have to find bounds based on equations and then use those answers to attach to an integral symbol. Basically I have found the bounds for r, theta, and z, I just do not know which one i have to integrate first (which variable goes on the inner most integral). Here is an example to make it easier to follow...
Evaluate the integral, where E is enclosed by the paraboloid z = 6 + x2 + y2, the cylinder x2 + y2 = 2, and the xy-plane. Use cylindrical coordinates.
So i know the z bounds are z = 6+r and z = 0....the r bounds are r = rad(2) and r = 0....and the theta bounds are ? = 0 and ? = 2? ...
the problem i am solving is this...
???e^z dV
I learned that the first variable you integrate by is theta, but i have no idea why that is the case. Please anyone who knows a trick or a way to tell which variable to integrate by first in problems like this one let me know... I just need to know this to get a complete grasp on triple integrals
z =6+ r^2..woops.. but thats not important
Evaluate the integral, where E is enclosed by the paraboloid z = 6 + x2 + y2, the cylinder x2 + y2 = 2, and the xy-plane. Use cylindrical coordinates.
So i know the z bounds are z = 6+r and z = 0....the r bounds are r = rad(2) and r = 0....and the theta bounds are ? = 0 and ? = 2? ...
the problem i am solving is this...
???e^z dV
I learned that the first variable you integrate by is theta, but i have no idea why that is the case. Please anyone who knows a trick or a way to tell which variable to integrate by first in problems like this one let me know... I just need to know this to get a complete grasp on triple integrals
z =6+ r^2..woops.. but thats not important