limits of integration

Question

In geometry, you learn that the volume of a cylinder is given by V = πr2h, where r is the radius and h is the height of the cylinder. Use integration in cylindrical coordinates to confirm the formula V. To do so, let r = 1 and h = 2, and fill in the limits in the integration below. Integrate, then compare the results (one from V and one from integration).

 

∫∫∫1¦r dz dr d∅

 

 

Answer 1

Given the order of your variables, you would use z=0 to z=2, and in the polar xy-plane, r=0 to r=1 and t=0 to t= 2pi. (t for theta)