
Integration Techniques and Substitution

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Mathematics
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10th - 12th Grade
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Hard
Standards-aligned

Lucas Foster
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Standards-aligned
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When using the substitution method for definite integrals, under what condition do you need to find new limits of integration?
When the anti-derivative is in terms of 'u'.
When the function is linear.
When the anti-derivative is in terms of 'x'.
When the integral is indefinite.
Tags
CCSS.HSF-BF.A.1C
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the substitution example, what is the inner function that is substituted with 'u'?
4x
6x
3x^2 + 1
x^2
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the differential 'du' equal to in terms of 'dx' in the given example?
2x dx
3x dx
4x dx
6x dx
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you determine the new lower limit of integration in terms of 'u' when x = 0?
u = 0
u = 6
u = 1
u = 3
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the new upper limit of integration in terms of 'u' when x = 2?
u = 9
u = 15
u = 13
u = 11
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the anti-derivative of 'u^2' in terms of 'u'?
u^4 / 4
u^3 / 2
u^2 / 2
u^3 / 3
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of evaluating the integral using the limits in terms of 'x'?
512
1024
488
256
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