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...
Related questions
Question
Find the area between 0 and 10
![The image displays a definite integral:
\[
\int_{0}^{10} -1.2 \, dx
\]
### Explanation
This integral represents the area under the constant function \( f(x) = -1.2 \) from \( x = 0 \) to \( x = 10 \).
- **Function Description**: The function \( f(x) = -1.2 \) is a horizontal line located at \(-1.2\) on the y-axis.
- **Integral Calculation**:
- The integral of a constant \( c \) over an interval \([a, b]\) is given by:
\[
\int_{a}^{b} c \, dx = c \times (b - a)
\]
- Applying this formula here:
\[
\int_{0}^{10} -1.2 \, dx = -1.2 \times (10 - 0) = -12
\]
- **Graphical Interpretation**: The graph of \( f(x) = -1.2 \) spans from \( x = 0 \) to \( x = 10 \), forming a rectangle below the x-axis with a height of \(-1.2\). The value \(-12\) represents the net area of this region, indicating that the entire area is negative due to its position below the x-axis.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6fe93ee-4f9e-427b-be03-0c98047db01a%2Fa6106aea-9fa9-45df-936e-90e8fd360bd6%2Ftgj6r1.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays a definite integral:
\[
\int_{0}^{10} -1.2 \, dx
\]
### Explanation
This integral represents the area under the constant function \( f(x) = -1.2 \) from \( x = 0 \) to \( x = 10 \).
- **Function Description**: The function \( f(x) = -1.2 \) is a horizontal line located at \(-1.2\) on the y-axis.
- **Integral Calculation**:
- The integral of a constant \( c \) over an interval \([a, b]\) is given by:
\[
\int_{a}^{b} c \, dx = c \times (b - a)
\]
- Applying this formula here:
\[
\int_{0}^{10} -1.2 \, dx = -1.2 \times (10 - 0) = -12
\]
- **Graphical Interpretation**: The graph of \( f(x) = -1.2 \) spans from \( x = 0 \) to \( x = 10 \), forming a rectangle below the x-axis with a height of \(-1.2\). The value \(-12\) represents the net area of this region, indicating that the entire area is negative due to its position below the x-axis.
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