Example 2

Evaluate

where E is the region shown in Figure 12.6.5,

0 ≤ x ≤ π/2, 0 ≤ y ≤ sin x, 0 ≤ z ≤ y cos x.

Figure 12.6.5

SOLUTION

We first evaluate the inside integral.

Now we evaluate the second integral.

Finally we evaluate the outside integral.