(a) Use the figure to find the [ f(x)dx. -3 value of VA f(x) dx? L²₁ f(x) dx = = -10 (b) If the area of the shaded region is A, what is L -3 4 A [ f(x)}d(x) = 4/ 2 X f(x) 8
(a) Use the figure to find the [ f(x)dx. -3 value of VA f(x) dx? L²₁ f(x) dx = = -10 (b) If the area of the shaded region is A, what is L -3 4 A [ f(x)}d(x) = 4/ 2 X f(x) 8
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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Need help with part (b)
![## Educational Content Transcription
### Problem Statement
**(a)** Use the figure to find the value of \( \int_{-3}^{0} f(x) \, dx \).
\[ \int_{-3}^{0} f(x) \, dx = -10 \] ✔️
**(b)** If the area of the shaded region is \( A \), what is \( \int_{-3}^{4} f(x) \, dx \)?
\[ \int_{-3}^{4} f(x) \, dx = \frac{A}{2} \] ❌
### Graph Explanation
The graph depicts a function \( f(x) \) plotted over the \( x \)-axis ranging from \( x = -4 \) to \( x = 5 \). The curve of the function oscillates around the horizontal axis, crossing it at several points:
- The function begins decreasing from \( x = -4 \) to \( x = -3 \) and passes below the axis.
- There are waving patterns for \( x \) between \( -3 \) and \( 0 \) as well as between \( 0 \) and the positive x-values, with peaks and troughs invariant over the length.
- The region between \( x = 3 \) and \( x = 4 \) is shaded, indicative of specific interest for calculation. This region lies below the horizontal axis.
The shaded region, which is here considered in part **(b)**, signifies area calculations that may contribute to evaluating definite integrals over specified limits on the \( x \)-axis.
### Key Observations
- In part **(a)**, the correct value for the integral over the interval \([-3, 0]\) is provided as \(-10\).
- In part **(b)**, the expression attempting to equate the integral over \([-3, 4]\) to \(\frac{A}{2}\) is marked incorrect.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe59facd3-ea8e-4c1d-9c3a-436e1d3f8729%2F77d17eeb-2361-4021-8455-cbf62345c06f%2F7az386a_processed.png&w=3840&q=75)
Transcribed Image Text:## Educational Content Transcription
### Problem Statement
**(a)** Use the figure to find the value of \( \int_{-3}^{0} f(x) \, dx \).
\[ \int_{-3}^{0} f(x) \, dx = -10 \] ✔️
**(b)** If the area of the shaded region is \( A \), what is \( \int_{-3}^{4} f(x) \, dx \)?
\[ \int_{-3}^{4} f(x) \, dx = \frac{A}{2} \] ❌
### Graph Explanation
The graph depicts a function \( f(x) \) plotted over the \( x \)-axis ranging from \( x = -4 \) to \( x = 5 \). The curve of the function oscillates around the horizontal axis, crossing it at several points:
- The function begins decreasing from \( x = -4 \) to \( x = -3 \) and passes below the axis.
- There are waving patterns for \( x \) between \( -3 \) and \( 0 \) as well as between \( 0 \) and the positive x-values, with peaks and troughs invariant over the length.
- The region between \( x = 3 \) and \( x = 4 \) is shaded, indicative of specific interest for calculation. This region lies below the horizontal axis.
The shaded region, which is here considered in part **(b)**, signifies area calculations that may contribute to evaluating definite integrals over specified limits on the \( x \)-axis.
### Key Observations
- In part **(a)**, the correct value for the integral over the interval \([-3, 0]\) is provided as \(-10\).
- In part **(b)**, the expression attempting to equate the integral over \([-3, 4]\) to \(\frac{A}{2}\) is marked incorrect.
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