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201092 USAIG 30. The graph of g consists of two straight lines and a semi- circle. Use it to evaluate each integral. 6 (a) f g(x) dx (b) g(x) dx (c) f g(x) dx gaib die raz pust pigme on -ST051 100% GE 2- ***0 bro igh dor Casiq Ismlosb . obmy=g(x) ionbin on 01 Union V 8 Soni bait (s) + 27% xie dow

201092 USAIG 30. The graph of g consists of two straight lines and a semi- circle. Use it to evaluate each integral. 6 (a) f g(x) dx (b) g(x) dx (c) f g(x) dx gaib die raz pust pigme on -ST051 100% GE 2- ***0 bro igh dor Casiq Ismlosb . obmy=g(x) ionbin on 01 Union V 8 Soni bait (s) + 27% xie dow

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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The picture is the problem *Please use handwriting not typing, I understand it better that way, thank you*
**Exercise 30: Evaluating Integrals Using a Graph** The graph of \( g(x) \) consists of two straight lines and a semicircle. Use this graph to evaluate each integral. **Integrals to Evaluate:** (a) \( \int_{0}^{2} g(x) \, dx \) (b) \( \int_{2}^{6} g(x) \, dx \) (c) \( \int_{0}^{7} g(x) \, dx \) **Graph Explanation:** - **Axes:** The x-axis and y-axis are labeled, with the x-axis ranging from 0 to 7 and the y-axis ranging from 0 to 4. - **Lines and Semicircle:** - A straight line descends from \( y = 4 \) at \( x = 0 \) to \( y = 0 \) at \( x = 2 \). - A semicircle arcs from \( x = 2 \) to \( x = 6 \), centered at \( x = 4 \) with a radius of 2. - A straight line ascends from the endpoint of the semicircle at \( x = 6 \) back to \( y = 2 \) at \( x = 7 \). The diagram provides visual information needed to calculate the integrals by summing up the areas under the pieces of the graph within the given intervals.
Transcribed Image Text:**Exercise 30: Evaluating Integrals Using a Graph** The graph of \( g(x) \) consists of two straight lines and a semicircle. Use this graph to evaluate each integral. **Integrals to Evaluate:** (a) \( \int_{0}^{2} g(x) \, dx \) (b) \( \int_{2}^{6} g(x) \, dx \) (c) \( \int_{0}^{7} g(x) \, dx \) **Graph Explanation:** - **Axes:** The x-axis and y-axis are labeled, with the x-axis ranging from 0 to 7 and the y-axis ranging from 0 to 4. - **Lines and Semicircle:** - A straight line descends from \( y = 4 \) at \( x = 0 \) to \( y = 0 \) at \( x = 2 \). - A semicircle arcs from \( x = 2 \) to \( x = 6 \), centered at \( x = 4 \) with a radius of 2. - A straight line ascends from the endpoint of the semicircle at \( x = 6 \) back to \( y = 2 \) at \( x = 7 \). The diagram provides visual information needed to calculate the integrals by summing up the areas under the pieces of the graph within the given intervals.
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