   Chapter 14.3, Problem 14E

Chapter
Section
Textbook Problem

Evaluating a Double Integral in Exercises 9-16, evaluate the double Integral ∫ R ∫ f ( r , θ ) d A and sketch the region R. ∫ 0 π / 2 ∫ 0 3 r e − r 2   d r   d θ

To determine

To calculate: What the value of the given double integral Rf(r,θ)dA=0π/203rer2drdθ will be. Also, sketch the region R.

Explanation

Given:

The double integral Rf(r,θ)dA=0π/203rer2drdθ.

Calculation:

Now, take the double integral 0π/203rer2drdθ

Put r2=t, then

2rdr=dt

0π/203rer2drdθ=0π/209et2dtdθ=120π/2[et]

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