
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
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.](https://content.bartleby.com/qna-images/question/d6fe93ee-4f9e-427b-be03-0c98047db01a/a6106aea-9fa9-45df-936e-90e8fd360bd6/tgj6r1.jpeg)
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.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 2 steps with 2 images

Knowledge Booster
Similar questions
- Determine the value of z such that the area to the right of z is 0.9906. Round the solution to two decimal places, as z-values are traditionally rounded. Zarrow_forwardFind the area under a normal curve to the right of z = -2.72. 0.9752 O 0.9967 0.9078 O 0.9231 QUESTION 13 Find the area to the left of z = 1.28. 0.8997 0.8092 O 0.9902 O 0.9905arrow_forwardFind z when the area to the left of z is .05.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning

Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning

Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON

Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON

Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman


Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning