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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![The problem presented on the page is a calculus exercise involving definite integrals. The given information is:
1. \(\int_{2}^{6} f(x) \, dx = 7.3\)
2. \(\int_{2}^{4} f(x) \, dx = 5.9\)
The task is to find \(\int_{4}^{6} f(x) \, dx\).
To solve this, we can use the property of definite integrals that states:
\[
\int_{a}^{c} f(x) \, dx = \int_{a}^{b} f(x) \, dx + \int_{b}^{c} f(x) \, dx
\]
In our context, this means:
\[
\int_{2}^{6} f(x) \, dx = \int_{2}^{4} f(x) \, dx + \int_{4}^{6} f(x) \, dx
\]
We know the values of the integrals from 2 to 6 and from 2 to 4. Let's use these values:
\[
7.3 = 5.9 + \int_{4}^{6} f(x) \, dx
\]
We can solve for \(\int_{4}^{6} f(x) \, dx\) by subtracting 5.9 from 7.3:
\[
\int_{4}^{6} f(x) \, dx = 7.3 - 5.9 = 1.4
\]
Thus, \(\int_{4}^{6} f(x) \, dx = 1.4\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8dcb78da-3870-4da6-8da3-7759b1e48992%2F2d52d4d8-ec04-4716-beb2-8af1ae7ccbf5%2Fd8zj50g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The problem presented on the page is a calculus exercise involving definite integrals. The given information is:
1. \(\int_{2}^{6} f(x) \, dx = 7.3\)
2. \(\int_{2}^{4} f(x) \, dx = 5.9\)
The task is to find \(\int_{4}^{6} f(x) \, dx\).
To solve this, we can use the property of definite integrals that states:
\[
\int_{a}^{c} f(x) \, dx = \int_{a}^{b} f(x) \, dx + \int_{b}^{c} f(x) \, dx
\]
In our context, this means:
\[
\int_{2}^{6} f(x) \, dx = \int_{2}^{4} f(x) \, dx + \int_{4}^{6} f(x) \, dx
\]
We know the values of the integrals from 2 to 6 and from 2 to 4. Let's use these values:
\[
7.3 = 5.9 + \int_{4}^{6} f(x) \, dx
\]
We can solve for \(\int_{4}^{6} f(x) \, dx\) by subtracting 5.9 from 7.3:
\[
\int_{4}^{6} f(x) \, dx = 7.3 - 5.9 = 1.4
\]
Thus, \(\int_{4}^{6} f(x) \, dx = 1.4\).
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