a. Suppose that the function c(x) = 200+ 100e-0.1x models the density of traffic on a straight road, measured in cars per mile, where x is number of miles east of a major interchange, and consider the definite integral (200 + 100e-0.1x) dx. i. What are the units on the product c(x). Ax? ii. What are the units on the definite integral and its Riemann sum approxi- mation given by [²0(x) dx = {c{x}^x? Σc(x;)Ax? i=1 iii. Evaluate the definite integral ² c(x) dx = ² (200 + 100e-0.1x) dx and write one sentence to explain the meaning of the value you find.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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a. Suppose that the function c(x) = 200+100e-0.¹x models the density of traffic on
a straight road, measured in cars per mile, where x is number of miles east of a
major interchange, and consider the definite integral ² (200 + 100e-0.¹1x) dx.
i. What are the units on the product c(x) · Ax?
.
ii. What are the units on the definite integral and its Riemann sum approxi-
mation given by
n
[² * c(x) dx = c(x;)Ax?
i=1
iii. Evaluate the definite integral ² c(x) dx = ² (200 + 100e-0.¹x) dx and write
one sentence to explain the meaning of the value you find.
Transcribed Image Text:a. Suppose that the function c(x) = 200+100e-0.¹x models the density of traffic on a straight road, measured in cars per mile, where x is number of miles east of a major interchange, and consider the definite integral ² (200 + 100e-0.¹1x) dx. i. What are the units on the product c(x) · Ax? . ii. What are the units on the definite integral and its Riemann sum approxi- mation given by n [² * c(x) dx = c(x;)Ax? i=1 iii. Evaluate the definite integral ² c(x) dx = ² (200 + 100e-0.¹x) dx and write one sentence to explain the meaning of the value you find.
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