Chapter 14.3, Problem 14E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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 âˆ«Râˆ«f(r,Î¸)dA=âˆ«0Ï€/2âˆ«03reâˆ’r2drdÎ¸.

Calculation:

Now, take the double integral âˆ«0Ï€/2âˆ«03reâˆ’r2drdÎ¸

Put âˆ’r2=t, then

âˆ’2rdr=dt

âˆ«0Ï€/2âˆ«03reâˆ’r2drdÎ¸=âˆ«0Ï€/2âˆ«0âˆ’9âˆ’et2dtdÎ¸=âˆ’12âˆ«0Ï€/2[et]

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