Using an appropriate coordinate system, evaluate the integral where Q is the region inside the cylinder and between the planes and .

Question

Using an appropriate coordinate system, evaluate the integral  where Q is the region inside the cylinder  and between the planes  and  .

Quizplus · Accepted Answer

We need to evaluate the integral over the region Q which is a cylinder, and between the planes z=2 and z=3. Thus, the best coordinate system to use is cylindrical coordinates. The limits of integration for this system are rho from 0 to 1, theta from 0 to 2*pi, and z from 2 to 3.

Thus, the integral can be written as:

∫∫∫Q 11eaa88b_92f6_ce87_a696_ebb6e40ba31f_TB5869_11 dV
= ∫0^1 ∫0^2π ∫2^3 11eaa88b_92f6_ce87_a696_ebb6e40ba31f_TB5869_11 rz dz dθ drho
= 11eaa88b_92f7_43bc_a696_59df3c50b296_TB5869_11 (approx. 7.389)

Thus, the correct choice is B.

Using an Appropriate Coordinate System, Evaluate the Integral Where