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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Evaluate the double integral by first identifying it as the volume of a solid.

10. R ( 2 x + 1 ) d A , R = { ( x , y ) | 0 x 2 , 0 y 4 }

To determine

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

Explanation

Given:

The function is f(x,y)=2x+1 .

The rectangular region, R={(x,y)|0x2,0y4} .

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 x is positive and f(x,y)=2x+1 is greater than 0, it is enough to find the value of double integral in order to find the volume of the solid.

R(2x+1)dA=02[04(2x+1)dy]dx=02

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Chapter 15 Solutions

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