   Chapter 15.3, Problem 6E

Chapter
Section
Textbook Problem

Sketch the region whose area is given by the integral and evaluate the integral.6. ∫ π / 2 π ∫ 0 2   sin θ r   d r   d θ

To determine

To sketch: The outline of the solid whose volume is given by the iterated integral and then evaluate the integral.

Explanation

Given:

The iterated integral, π2π02sinθrdrdθ .

Calculation:

From the given integral, it is observed that r varies from 0 to 2sinθ and θ varies from π2 to π So, the graph can be drawn as given below in Figure 1.

Integrate the given integral.

π2π02sinθrdrdθ=π2π[r22]02sinθdθ=π2π[(2sinθ)22(0)22]dθ=

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