The figure shows the area of regions bounded by the graph of f and the x-axis. Evaluate the integral. f(x) y = f(x) 13 9. A) -5 B) 13 C) 5 D) -13
The figure shows the area of regions bounded by the graph of f and the x-axis. Evaluate the integral. f(x) y = f(x) 13 9. A) -5 B) 13 C) 5 D) -13
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 image illustrates a problem involving the evaluation of an integral. The task is to find the value of the integral of the function \( f(x) \) from \( a \) to \( c \).
**Description of Graph:**
- The graph depicts the curve \( y = f(x) \).
- The areas between the curve and the x-axis are shaded, indicating integration regions.
- The area from \( a \) to \( b \) (between the curve and the x-axis) is given as 13 units above the x-axis.
- The area from \( b \) to \( c \) (below the x-axis) is 9 units.
- An additional area from \( b \) to \( c \) is 4 units above the x-axis.
**Problem Statement:**
Evaluate the definite integral:
\[
\int_{a}^{c} f(x)
\]
**Multiple Choice Options:**
- A) -5
- B) 13
- C) 5
- D) -13
**Extra Information:**
The instructions request a detailed showing of the work, despite its simplicity, with the potential to earn an additional 3 points.
**Solution Approach:**
The value of \(\int_{a}^{c} f(x) \, dx\) is calculated as the sum of the shaded areas, considering the sign based on their position relative to the x-axis:
- The area from \(a\) to \(b\) contributes +13.
- The area from \(b\) to \(c\) has two parts:
- A negative contribution of -9 (below the x-axis).
- A positive contribution of +4 (above the x-axis).
\[
\int_{a}^{c} f(x) \, dx = 13 - 9 + 4 = 8
\]
Since none of the options match 8, there may be missing context. Review the problem to ensure all components are appropriately considered.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6316f2e9-b377-432e-9092-cf1a3f72da1c%2Fa57f08de-ee54-4c60-ad44-d5da51c064dd%2F2nps0bzo_processed.png&w=3840&q=75)
Transcribed Image Text:The image illustrates a problem involving the evaluation of an integral. The task is to find the value of the integral of the function \( f(x) \) from \( a \) to \( c \).
**Description of Graph:**
- The graph depicts the curve \( y = f(x) \).
- The areas between the curve and the x-axis are shaded, indicating integration regions.
- The area from \( a \) to \( b \) (between the curve and the x-axis) is given as 13 units above the x-axis.
- The area from \( b \) to \( c \) (below the x-axis) is 9 units.
- An additional area from \( b \) to \( c \) is 4 units above the x-axis.
**Problem Statement:**
Evaluate the definite integral:
\[
\int_{a}^{c} f(x)
\]
**Multiple Choice Options:**
- A) -5
- B) 13
- C) 5
- D) -13
**Extra Information:**
The instructions request a detailed showing of the work, despite its simplicity, with the potential to earn an additional 3 points.
**Solution Approach:**
The value of \(\int_{a}^{c} f(x) \, dx\) is calculated as the sum of the shaded areas, considering the sign based on their position relative to the x-axis:
- The area from \(a\) to \(b\) contributes +13.
- The area from \(b\) to \(c\) has two parts:
- A negative contribution of -9 (below the x-axis).
- A positive contribution of +4 (above the x-axis).
\[
\int_{a}^{c} f(x) \, dx = 13 - 9 + 4 = 8
\]
Since none of the options match 8, there may be missing context. Review the problem to ensure all components are appropriately considered.
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