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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Rate of Change
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![g(x) dx
Step 1
If g(x) is positive, then the integral
g(x) dx corresponds to the area beneath g(x) and above the x-axis
over the interval [a, b].
On [0, 4], the function g(x) is above the x-axis and is therefore positive. Thus,
g(x) dx equals the area of
the triangle created by the function, the x-axis, and the y-axis.
This triangle is a right triangle with a side length of
4 along the x-axis and a side length of 8
8 along the y-axis. (Give the numeric values.)
Step 2
5b-h
then our triangle has an
Since the area of a triangle with base b and height h is A =
2
Thus,
g(x) dx =
area of
Submit
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Transcribed Image Text:g(x) dx
Step 1
If g(x) is positive, then the integral
g(x) dx corresponds to the area beneath g(x) and above the x-axis
over the interval [a, b].
On [0, 4], the function g(x) is above the x-axis and is therefore positive. Thus,
g(x) dx equals the area of
the triangle created by the function, the x-axis, and the y-axis.
This triangle is a right triangle with a side length of
4 along the x-axis and a side length of 8
8 along the y-axis. (Give the numeric values.)
Step 2
5b-h
then our triangle has an
Since the area of a triangle with base b and height h is A =
2
Thus,
g(x) dx =
area of
Submit
Skip (you cannot come back)
![8.
y = g(x)
4
8
14
Exercise (a)
g(x) dx
Step 1
If g(x) is positive, then the integral
g(x) dx corresponds to the area beneath g(x) and above the x-axis
over the interval [a, b].
g(x) dx equals the area of
On [0, 4], the function g(x) is above the x-axis and is therefore positive. Thus,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d5901db-f08a-493a-a04d-15d0534348e1%2F66ae690d-3984-424f-b3b2-dd47a4e4fa5d%2Fif2fqeo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8.
y = g(x)
4
8
14
Exercise (a)
g(x) dx
Step 1
If g(x) is positive, then the integral
g(x) dx corresponds to the area beneath g(x) and above the x-axis
over the interval [a, b].
g(x) dx equals the area of
On [0, 4], the function g(x) is above the x-axis and is therefore positive. Thus,
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