Question

Evaluate the following integral.

∬∫(xy + xz + yz) dV ; D = {(x, y, z): -1 ≤ x ≤ 1, -6 ≤ y ≤ 6, -7 ≤ z ≤ 7}

Answer 1

To evaluate the given integral over the given region D, we need to use the triple integral and substitute the limits of integration.

Step-by-step explanation:

To evaluate the given integral ∬(xy + xz + yz) dV over the region D = {(x, y, z): -1 ≤ x ≤ 1, -6 ≤ y ≤ 6, -7 ≤ z ≤ 7}, we will use the triple integral from multivariable calculus.

First, we write the integral as ∬∬∬(xy + xz + yz) dx dy dz.

Since the limits of integration for the variables x, y, and z are given, we can simply substitute these limits into the integral and evaluate it step by step.