
Integration by Substitution Concepts
Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
Mia Campbell
FREE Resource
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9 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main goal of using integration by substitution?
To solve differential equations
To differentiate the function
To simplify the integral by changing variables
To find the limit of the function
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When using integration by substitution, what is the first step?
Differentiate the function
Choose a substitution variable 'u'
Integrate directly
Find the derivative of 'u'
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the substitution method, what does 'du' represent?
The constant of integration
The original function
The integral of 'u'
The derivative of 'u' with respect to 'x'
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you handle the differential 'dx' in the substitution process?
Multiply it by 'u'
Express 'dx' in terms of 'du'
Ignore it
Replace it with 'du' directly
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the antiderivative of 1/u with respect to 'u'?
1/u + C
u^2/2
e^u + C
ln|u| + C
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
After finding the antiderivative in terms of 'u', what is the next step?
Find the limit
Convert back to the original variable 'x'
Differentiate the result
Solve for 'u'
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the final form of the antiderivative in terms of 'x' for the given example?
ln|5x + 1| + C
5/2 ln|x - 1| + C
2/5 ln|5x - 1| + C
2 ln|x - 5| + C
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