
Definite Integral Evaluation using U-Substitution
Interactive Video
•
Mathematics
•
9th - 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
Why is u-substitution necessary for evaluating the given integral?
Because the integrand is a constant function.
Because the integrand is the sine of one-half x.
Because the integrand is the sine of x.
Because the integrand is a simple polynomial.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the differential du in terms of dx for the substitution u = 1/2 x?
du = 1/2 dx
du = 2 dx
du = dx
du = 3 dx
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you adjust the limits of integration when using u-substitution?
By keeping the original limits of x.
By substituting the x-values into u = 1/2 x.
By multiplying the limits by 2.
By adding 1 to each limit.
Tags
CCSS.HSF.TF.B.7
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the antiderivative of sine u?
cosine u
-cosine u
sine u
-sine u
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of the definite integral after evaluating using u-substitution?
8
2
0
4
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the antiderivative expressed when evaluating directly in terms of x?
2 cosine (1/2 x)
-2 cosine (1/2 x)
-2 cosine x
2 sine (1/2 x)
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of the integral when evaluated directly in terms of x?
0
4
8
2
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