Chapter 15.4, Problem 1E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Electric charge is distributed over the rectangle 0 ≤ *x* ≤ 5, 2 ≤ *y* ≤ 5 so that the charge density at (*x*, *y*) is *σ*(*x*, *y*) = *2x* + 4*y* (measured in coulombs per square meter). Find the total charge on the rectangle.

To determine

**To find:** The total charge over the given rectangular region.

Explanation

**Given:**

The rectangle *R* is

The charge density at

**Formula used:**

The total charge *Q* on the given rectangular region *R* is,

Here, the charge density is given by

**Calculation:**

Total charge *Q* on the given rectangle *R* is,

Integrate with respect to *y,*

Apply the limit value of *y,*

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