Chapter 14.7, Problem 4E

### 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 Triple Iterated Integral In Exercises 3-8, evaluate the triple iterated integral. ∫ 0 π / 4 ∫ 0 6 ∫ 0 6 − r r z   d z   d r   d θ

To determine

To calculate: The value of provided triple iterated integral 0π40606rrzdzdrdθ

Explanation

Given:

The provided iterated integral is âˆ«0Ï€4âˆ«06âˆ«06âˆ’rrzdzdrdÎ¸

Formula used:

Use the integration formula

âˆ«xndx=xn+1n+1

And,

(aâˆ’b)2=a2âˆ’2ab+b2

Calculation:

Now, First Integrate the function with respect to z taking r as a constant variable then substitute the limit of z.

Then again integrate the obtained function with respect to r and substitute its limits.

Now, again integrate with respect to Î¸ and substitute its limit to get the result.

âˆ«0Ï€4âˆ«06âˆ«06âˆ’rrzdzdrdÎ¸=âˆ«0Ï€4âˆ«06[rz22]06âˆ’rdrdÎ¸=âˆ«0Ï€4âˆ«06(r(6âˆ’r)22âˆ’0)drd<

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