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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Comparing Different Orders of Integration In Exercises 7-12, set up the integrals for both orders of integration and use the more convenient order to find the volume of the solid region bounded by the surface f(x, y) and the planes. See Example 2.

f ( x , y ) = y 1 + x 2

Planes: z = 0 , y = 0 , y = x , x = 4

To determine

To calculate: The value of the function is f(x,y)=y1+x2 and points are z=0,y=0,y=x,x=4,x=0 by representing its integral for both orders.

Explanation

Given Information:

Function is f(x,y)=y1+x2 and points are z=0,y=0,y=x,x=4,x=0.

Formula used:

Standard form of volume integral

V=f(x,y)dxdy

Calculation:

Consider the primary equation and substitute the given function

V=y1+x2dydx

Consider case 1:

(1)x=04[0x(y1+x2)dy]dx

Consider case 1:

(2)y=016[y24(y1+x2

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