Solved: ?In the following exercises, change the order of integration and evaluate the

Chapter 5, Problem 113

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In the following exercises, change the order of integration and evaluate the integral.

Let  \(S_{1}\) and \(S_{2}\) be the solids situated in the first octant under the planes 2x + 2y + z = 2 and x + y + z = 1, respectively, and let S be the solid situated between \(S_{1}, S_{2}, x=0\) and y = 0.

a. Find the volume of the solid \(S_{1}\)

b. Find the volume of the solid \(S_{2}\)

c. Find the volume of the solid S by subtracting the volumes of the solids \(S_{1}\) and \(S_{2}\)

Text Transcription:

S_1

S_2

 S_1,S_2,x=0

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