Given the functions f(x)=x²-3x+2 and g(x)=8-2x, write the integral to find the area of the region pictured below that is bounded above by f(x) and g(x) and bounded below by the z-axis when integrating with respect to y. Do not evaluate the integral. Provide your answer below: dy 7 6+ 5+ 2 1 -6 -5-4-3 -2 -1 0 -1 -2- +++ -5 -6- -7 1 2 f(x) 5 6 7

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Given the functions f(x)=x²-3x+2 and g(x)=8-2x, write the integral to find the area of the region pictured
below that is bounded above by f(x) and g(x) and bounded below by the x-axis when integrating with respect to y.
Do not evaluate the integral.
Provide your answer below:
-7 -6 -5 -4
-3
-2 -1
7-
6
y
5+
14.
2
+
0
-1
-2-
-3-
-4+
-5-
-6-
-7-
1
2
3
4
5
6
g(x)
7
J
Transcribed Image Text:Question Given the functions f(x)=x²-3x+2 and g(x)=8-2x, write the integral to find the area of the region pictured below that is bounded above by f(x) and g(x) and bounded below by the x-axis when integrating with respect to y. Do not evaluate the integral. Provide your answer below: -7 -6 -5 -4 -3 -2 -1 7- 6 y 5+ 14. 2 + 0 -1 -2- -3- -4+ -5- -6- -7- 1 2 3 4 5 6 g(x) 7 J
Expert Solution
Step 1

f(x)=x2-3x+2

g(x)=8-2x

First of all, we have to write the functions in terms of y.

Consider the function: f(x)=x2-3x+2

 y=x2-3x+2

Now, solve for x in terms of y:

y=x2-3x+2

y=x2-2×1.5x+2

y=x2-2×1.5x+1.52-1.52+2

y=x-1.5^2-2.25+2

y=x-1.5^2-0.25

x-1.5^2=y+0.25

Take square root on both sides:

x-1.5=y+0.25

x=y+0.25+1.5

Now, this can be written as:

f(y)=y+0.25+1.5

 

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