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Chapter 13: Q. 36 (page 1015)

find the volume of the solid bounded above by the given function over the specified region

f(x,y)=10鈭�2x+y, with惟the region from Exercise 22.

Short Answer

Expert verified

The volume of the function is:54cubic inches.

Step by step solution

01

Step 1. Given information

The function:

f(x,y)=10-2x+y

The region in exercise 22

02

Step 2. To setup integral 

In the given region the -x鈮�y鈮�xand 0鈮�x鈮�3

So, the volume of the function over specified region is:

V=鈭�03鈭�-xxf(x,y)dydx=鈭�03鈭�-xx10-2x+ydydx

03

Step 3. Evaluate integral

First integrate the function with respect to y.

鈭�-xx10-2x+ydy=10y-2xy+y22-xx=10x-2x2+x22--10x+2x2+x22=20x-4x2

Now integrate the above function of x with respect to x.

鈭�03(20x-4x2)dx=20x22-4x3303=10x2-43x303=10(3)2-43(3)3-0=90-36=54

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