Consider the integral / 3x* (25 + 1) dz. In the following, we will evaluate the integral using two methods. A. First, rewrite the integral by multiplying out the integrand: | 32* (z* + 1) dz =| 3x°9+3x*4 dz Then evaluate the resulting integral term-by-term: | 32 (2* + 1) dz = B. Next, rewrite the integral using the substitution w = 25 +1: | 3z* (z* + 1) dz =|| dw Evaluate this integral (and back-substitute for w) to find the value of the original integral: | 32* (2* + 1) dr =
Consider the integral / 3x* (25 + 1) dz. In the following, we will evaluate the integral using two methods. A. First, rewrite the integral by multiplying out the integrand: | 32* (z* + 1) dz =| 3x°9+3x*4 dz Then evaluate the resulting integral term-by-term: | 32 (2* + 1) dz = B. Next, rewrite the integral using the substitution w = 25 +1: | 3z* (z* + 1) dz =|| dw Evaluate this integral (and back-substitute for w) to find the value of the original integral: | 32* (2* + 1) dr =
Calculus: Early Transcendentals
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Chapter1: Functions And Models
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![Consider the integral
3x* (x° + 1) dr. In the following, we will evaluate the integral using two methods.
A. First, rewrite the integral by multiplying out the integrand:
/ 32* (* + 1) dz = /
3x4
3x^9+3x^4
dr
Then evaluate the resulting integral term-by-term:
| 32 (25 + 1) da =
3x4
B. Next, rewrite the integral using the substitution w = x +1:
25
3z* (r + 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!)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F595fe312-b34b-43d8-8e7d-fe35809787e4%2Fc2b4718f-aa80-4d54-83af-e6fa75c62e76%2Fv42w7n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the integral
3x* (x° + 1) dr. In the following, we will evaluate the integral using two methods.
A. First, rewrite the integral by multiplying out the integrand:
/ 32* (* + 1) dz = /
3x4
3x^9+3x^4
dr
Then evaluate the resulting integral term-by-term:
| 32 (25 + 1) da =
3x4
B. Next, rewrite the integral using the substitution w = x +1:
25
3z* (r + 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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