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Consider the integral 6x? (r + 1) dz. In the following, we will evaluate the integral using two methods. A. First, rewrite the integral by multiplying out the integrand: | 62? (2 + 1) dr = dr Then evaluate the resulting integral term-by-term: 6x? (2³ + 1) de = B. Next, rewrite the integral using the substitution w = r +1: 6x2 (r + 1) dr = | dw Evaluate this integral (and back-substitute for w) to find the value of the original integral: | 62* (2* + 1) dz = 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!)

Consider the integral 6x? (r + 1) dz. In the following, we will evaluate the integral using two methods. A. First, rewrite the integral by multiplying out the integrand: | 62? (2 + 1) dr = dr Then evaluate the resulting integral term-by-term: 6x? (2³ + 1) de = B. Next, rewrite the integral using the substitution w = r +1: 6x2 (r + 1) dr = | dw Evaluate this integral (and back-substitute for w) to find the value of the original integral: | 62* (2* + 1) dz = 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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Evaluate the integral in terms of the constant: z dz
Transcribed Image Text:Evaluate the integral in terms of the constant: z dz
Consider the integral 6x2 (2 + 1) dz. In the following, we will evaluate the integral using two methods. A. First, rewrite the integral by multiplying out the integrand: | 62 (2 + 1) dr = da Then evaluate the resulting integral term-by-term: | 62* (z' + 1) da = B. Next, rewrite the integral using the substitution w = x +1: 6x2 (r + 1) dr = | dw Evaluate this integral (and back-substitute for w) to find the value of the original integral: | 62* (2* + 1) dz = 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:Consider the integral 6x2 (2 + 1) dz. In the following, we will evaluate the integral using two methods. A. First, rewrite the integral by multiplying out the integrand: | 62 (2 + 1) dr = da Then evaluate the resulting integral term-by-term: | 62* (z' + 1) da = B. Next, rewrite the integral using the substitution w = x +1: 6x2 (r + 1) dr = | dw Evaluate this integral (and back-substitute for w) to find the value of the original integral: | 62* (2* + 1) dz = 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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