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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![**Question:**
Use the values
\[
\int_{0}^{2}f(x)dx = -2 \quad \text{and} \quad \int_{0}^{2}g(x)dx = 9
\]
to evaluate the definite integral
\[
\int_{0}^{2}[f(x) - 9g(x)]dx.
\]
**Options:**
a) \(-74\)
b) \(-83\)
c) \(79\)
d) \(18\)
e) \(0\)
**Solution Explanation:**
To solve the problem, apply the properties of definite integrals. Specifically, the linearity of integration:
\[
\int_{0}^{2}[f(x) - 9g(x)]dx = \int_{0}^{2}f(x)dx - 9\int_{0}^{2}g(x)dx
\]
Plug in the given integral values:
\[
= -2 - 9(9) = -2 - 81 = -83
\]
Therefore, the answer is option b) \(-83\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff0b581ba-098c-432d-a731-9ec346ce3593%2F61351a08-7fcf-4e86-b37e-973bbcd3a01f%2Fduxxo49_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
Use the values
\[
\int_{0}^{2}f(x)dx = -2 \quad \text{and} \quad \int_{0}^{2}g(x)dx = 9
\]
to evaluate the definite integral
\[
\int_{0}^{2}[f(x) - 9g(x)]dx.
\]
**Options:**
a) \(-74\)
b) \(-83\)
c) \(79\)
d) \(18\)
e) \(0\)
**Solution Explanation:**
To solve the problem, apply the properties of definite integrals. Specifically, the linearity of integration:
\[
\int_{0}^{2}[f(x) - 9g(x)]dx = \int_{0}^{2}f(x)dx - 9\int_{0}^{2}g(x)dx
\]
Plug in the given integral values:
\[
= -2 - 9(9) = -2 - 81 = -83
\]
Therefore, the answer is option b) \(-83\).
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