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
![The figure illustrates the area of regions bounded by the graph of \( f \) and the x-axis. The task is to evaluate the integral \( \int_a^c f(x) \, dx \).
**Graph Explanation:**
- The graph displays a function \( y = f(x) \) with three shaded regions between the curve and the x-axis.
- The area above the x-axis, from \( a \) to a point between \( a \) and \( b \), is labeled with an area of 9.
- The area below the x-axis, from this intermediate point to \( b \), is labeled with an area of 5.
- The area above the x-axis again, from \( b \) to \( c \), has an area of 4.
**Integral Evaluation:**
To evaluate the integral from \( a \) to \( c \), add the areas above the x-axis and subtract the area below the x-axis:
\[
\int_a^c f(x) \, dx = 9 - 5 + 4 = 8
\]
Considering options provided, select the closest applicable option:
- \( \circ \) 1
- \( \circ \) 9
- \( \circ \) -1
- \( \circ \) -9
In the given options, the integral may need reevaluation, or there might be an oversight in the options aligning with common calculus understanding. Please verify the integral calculation or consider potential typographical errors in the options.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6de7c9a-ee96-456f-9ad6-04e5123e73e5%2Fd6676f74-b848-4950-aeb0-67616b7021fe%2Fa7bm6j5_processed.png&w=3840&q=75)
Transcribed Image Text:The figure illustrates the area of regions bounded by the graph of \( f \) and the x-axis. The task is to evaluate the integral \( \int_a^c f(x) \, dx \).
**Graph Explanation:**
- The graph displays a function \( y = f(x) \) with three shaded regions between the curve and the x-axis.
- The area above the x-axis, from \( a \) to a point between \( a \) and \( b \), is labeled with an area of 9.
- The area below the x-axis, from this intermediate point to \( b \), is labeled with an area of 5.
- The area above the x-axis again, from \( b \) to \( c \), has an area of 4.
**Integral Evaluation:**
To evaluate the integral from \( a \) to \( c \), add the areas above the x-axis and subtract the area below the x-axis:
\[
\int_a^c f(x) \, dx = 9 - 5 + 4 = 8
\]
Considering options provided, select the closest applicable option:
- \( \circ \) 1
- \( \circ \) 9
- \( \circ \) -1
- \( \circ \) -9
In the given options, the integral may need reevaluation, or there might be an oversight in the options aligning with common calculus understanding. Please verify the integral calculation or consider potential typographical errors in the options.
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