Chapter 15.2, Problem 67E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Use geometry or symmetry, or both, to evaluate the double integral.

**67.**

*D* is the rectangle 0 ≤ *x* ≤ *a*, 0 ≤ *y* ≤ *b*

To determine

**To calculate:** The value of given double integral over
*.*

Explanation

**Given:**

The function is,

The domain *D* is the rectangle

**Calculation:**

From the given conditions,

The first integrand
*D.*

So the region obtained is a triangular cylinder with the length *b*. Note that each of the cross section has the base *a* and the height 2*a*

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