

Understanding U-Substitution in Integration
Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Liam Anderson
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main challenge in evaluating the given indefinite integral?
The integrand is a simple polynomial.
The integrand involves a trigonometric function.
The integrand is a rational function.
The integrand involves a product of a polynomial and a square root.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why does the initial u-substitution of u = x^3 not work?
It results in a differential that does not match the integrand.
It results in a differential that matches the integrand.
It simplifies the integral too much.
It introduces a trigonometric function.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What substitution is proposed after the initial attempt fails?
u = 15
u = x^2
u = x^2 + 15
u = x^3
Tags
CCSS.8.EE.A.2
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is x^2 expressed in terms of u in the new substitution?
x^2 = u + 15
x^2 = u - 15
x^2 = 15 + u
x^2 = 15 - u
Tags
CCSS.8.EE.A.2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the next step after rewriting the integral using the new substitution?
Using partial fraction decomposition.
Applying the chain rule.
Performing integration by parts.
Distributing the u to the 1/2.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of integrating u to the 3/2?
u to the 4/3 divided by 4/3
u to the 1/2 divided by 1/2
u to the 2/3 divided by 2/3
u to the 5/2 divided by 5/2
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the constant factor 1/2 handled in the integration process?
It is ignored.
It is multiplied with the integral.
It is added to the integral.
It is subtracted from the integral.
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