
U-Substitution in Definite Integrals
Interactive Video
•
Mathematics
•
11th - 12th Grade
•
Practice Problem
•
Hard
Liam Anderson
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in evaluating a definite integral using u-substitution?
Graphing the function
Changing the limits of integration
Rewriting the integrand with a rational exponent
Finding the antiderivative directly
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When performing u-substitution, what is typically chosen as u?
A part of the integrand that simplifies the derivative
The limits of integration
The constant factor in the integrand
The entire integrand
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you adjust the limits of integration when using u-substitution?
By subtracting the lower limit from the upper limit
By doubling the original limits
By converting them to u-values using the substitution equation
By keeping them the same as the original x-values
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the new form of the integrand function after substitution and simplification?
x to the power of one-half
u to the power of negative one-half
x to the power of negative one-half
u to the power of one-half
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the role of the constant factor when simplifying the integrand after substitution?
It is ignored
It is used to find the derivative
It is factored out of the integral
It is added to the limits of integration
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of the definite integral after evaluating the antiderivative?
Zero
One
Two
Four
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the antiderivative of u to the power of negative one-half found?
By graphing the function
By differentiating
By using the power rule for integration
By integrating directly
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