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(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
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.
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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