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Small changes in numbers in an integrand can result in very different methods required for integration. Consider the integral below. Assume b #0 but b could be positive or negative in the answers below. 1 x²+2x+b dx 1. What value of b would result in a u-substitution method where the power rule would be used? 2. What is one possible value of b where a u-substitution method is used resulting in an arctangent? 3. What is one possible value of b that would result in a partial fraction decomposition method being used? 4. Evaluate the integral with the b value that results in a partial fraction decomposition method. Upload your handwritten work for finding the values of b in questions 1-3 along with the work for evaluating the integral in the box below. Show detailed work for evaluating the integral and finding the decomposition.

Small changes in numbers in an integrand can result in very different methods required for integration. Consider the integral below. Assume b #0 but b could be positive or negative in the answers below. 1 x²+2x+b dx 1. What value of b would result in a u-substitution method where the power rule would be used? 2. What is one possible value of b where a u-substitution method is used resulting in an arctangent? 3. What is one possible value of b that would result in a partial fraction decomposition method being used? 4. Evaluate the integral with the b value that results in a partial fraction decomposition method. Upload your handwritten work for finding the values of b in questions 1-3 along with the work for evaluating the integral in the box below. Show detailed work for evaluating the integral and finding the decomposition.

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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Small changes in numbers in an integrand can result in very different methods required for integration. Consider the integral below. Assume b #0 but b could be positive or negative in the answers below. 1 x²+2x+b dx 1. What value of b would result in a u-substitution method where the power rule would be used? 2. What is one possible value of b where a u-substitution method is used resulting in an arctangent? 3. What is one possible value of b that would result in a partial fraction decomposition method being used? 4. Evaluate the integral with the b value that results in a partial fraction decomposition method. Upload your handwritten work for finding the values of b in questions 1-3 along with the work for evaluating the integral in the box below. Show detailed work for evaluating the integral and finding the decomposition.
Transcribed Image Text:Small changes in numbers in an integrand can result in very different methods required for integration. Consider the integral below. Assume b #0 but b could be positive or negative in the answers below. 1 x²+2x+b dx 1. What value of b would result in a u-substitution method where the power rule would be used? 2. What is one possible value of b where a u-substitution method is used resulting in an arctangent? 3. What is one possible value of b that would result in a partial fraction decomposition method being used? 4. Evaluate the integral with the b value that results in a partial fraction decomposition method. Upload your handwritten work for finding the values of b in questions 1-3 along with the work for evaluating the integral in the box below. Show detailed work for evaluating the integral and finding the decomposition.
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