   Chapter 15.1, Problem 11E

Chapter
Section
Textbook Problem

Evaluate the double integral by first identifying it as the volume of a solid.11. ∬ R ( 4 − 2 y ) d A ,   R = [ 0 , 1 ] × [ 0 , 1 ]

To determine

To estimate: The value of given double integral over the rectangular region R.

Explanation

Given:

The function is f(x,y)=42y .

The rectangular region is R=[0,1]×[0,1] .

Interpretation:

From the given f(x,y) and R, it is observed that the surface is a rectangular solid by surmounted by a triangular cylinder.

Calculation:

Since y is positive which lies between 0 to 1 and f(x,y)=42y is greater than 0, it is enough to find the value of double integral in order to find the volume of the solid

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