Consider the graph with the region shaded. How can you approximate the value of the definite integral? 2:5- 2- 1.5 1- f(x) 0.5 -0.5 0.5 1.5 2.5 3.5 4 4.5 5.5 -p.5-
Consider the graph with the region shaded. How can you approximate the value of the definite integral? 2:5- 2- 1.5 1- f(x) 0.5 -0.5 0.5 1.5 2.5 3.5 4 4.5 5.5 -p.5-
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the graph with the region shaded. How can you approximate the value of
the definite integral?
2.5-
2-
1.5-
1-
f(x)
0.5
-0.5
0.5
1.5
2.5
3.5
4
4.5
5.5
-0.5
-1-
-1.5
-2-
--2.5
-3-
![Sum the function values on the interval [O, 3].
Set up a Riemann Sum on the interval [0, 3].
Find the antiderivative of the function and then use the net change theorem
(fundamental theorem of calculus).
Find the average rate of change of the antiderivative of the function.
|Approximate the shaded area on the interval [0, 1] and approximate the area on
the interval [1, 3] and then take the sum of these two approximation.
Approximate the shaded area below the horizontal axis and subtract that area
from the area that is above the horizontal axis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe37d6a9f-32c9-4856-a6ed-e90ba5efa5a8%2Fc67e2962-0a07-4ccb-9728-ef859bf8219b%2Fzs5vnbn_processed.png&w=3840&q=75)
Transcribed Image Text:Sum the function values on the interval [O, 3].
Set up a Riemann Sum on the interval [0, 3].
Find the antiderivative of the function and then use the net change theorem
(fundamental theorem of calculus).
Find the average rate of change of the antiderivative of the function.
|Approximate the shaded area on the interval [0, 1] and approximate the area on
the interval [1, 3] and then take the sum of these two approximation.
Approximate the shaded area below the horizontal axis and subtract that area
from the area that is above the horizontal axis.
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