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A. First, rewrite the integral by multiplying out the integrand: | 3x° (x* + 1) dx = dx Then evaluate the resulting integral term-by-term: | 3x' (x* + 1) dx = B. Next, rewrite the integral using the substitution w = x* +1: | 3x' (x* + 1) dx = dw Evaluate this integral (and back-substitute for w) to find the value of the original integral: | 3x' (x* + 1) dx = C. How are your expressions from parts (A) and (B) different? What is the difference between the two? (Ignore the constant of integration.) (answer from B)- (answer from A) = Are both of the answers correct? (Be sure you can explain why they are!)

A. First, rewrite the integral by multiplying out the integrand: | 3x° (x* + 1) dx = dx Then evaluate the resulting integral term-by-term: | 3x' (x* + 1) dx = B. Next, rewrite the integral using the substitution w = x* +1: | 3x' (x* + 1) dx = dw Evaluate this integral (and back-substitute for w) to find the value of the original integral: | 3x' (x* + 1) dx = C. How are your expressions from parts (A) and (B) different? What is the difference between the two? (Ignore the constant of integration.) (answer from B)- (answer from A) = Are both of the answers correct? (Be sure you can explain why they are!)

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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A. First, rewrite the integral by multiplying out the integrand: 3x° (x* + 1) dx = | dx Then evaluate the resulting integral term-by-term: | 3x° (x* + 1) dx = B. Next, rewrite the integral using the substitution w = x* + 1: / 3x (x* + 1) dx = / dw Evaluate this integral (and back-substitute for w) to find the value of the original integral: | 3x (x* + 1) dx = C. How are your expressions from parts (A) and (B) different? What is the difference between the two? (Ignore the constant of integration.) (answer from B)- (answer from A) = Are both of the answers correct? (Be sure you can explain why they are!)
Transcribed Image Text:A. First, rewrite the integral by multiplying out the integrand: 3x° (x* + 1) dx = | dx Then evaluate the resulting integral term-by-term: | 3x° (x* + 1) dx = B. Next, rewrite the integral using the substitution w = x* + 1: / 3x (x* + 1) dx = / dw Evaluate this integral (and back-substitute for w) to find the value of the original integral: | 3x (x* + 1) dx = C. How are your expressions from parts (A) and (B) different? What is the difference between the two? (Ignore the constant of integration.) (answer from B)- (answer from A) = Are both of the answers correct? (Be sure you can explain why they are!)
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