Which integration technique is useful when the integrand is a product of a function and its derivative?

Trigonometric Substitution Techniques

Interactive Video
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Mathematics
•
11th - 12th Grade
•
Hard

Emma Peterson
FREE Resource
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Integration by parts
Trigonometric substitution
Partial fraction decomposition
Substitution rule
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the correct substitution for the expression √(A² - x²) in trigonometric substitution?
x = A cos θ
x = A sin θ
x = A tan θ
x = A sec θ
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In trigonometric substitution, which identity is used to simplify √(A² + x²)?
1 + tan² θ = sec² θ
sec² θ - 1 = tan² θ
1 - sin² θ = cos² θ
sin² θ + cos² θ = 1
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When converting back to x from θ, which trigonometric function is used if x = A sin θ?
sin θ
sec θ
tan θ
cos θ
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example of integrating √(9 - x²) / x², what is the substitution for x?
3 tan θ
3 sec θ
3 sin θ
3 cos θ
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of 3 sin θ with respect to θ?
3 tan θ
3 sec θ
3 sin θ
3 cos θ
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the second example, what substitution is made for x when simplifying √(x² + 4)?
x = 2 cos θ
x = 2 sec θ
x = 2 tan θ
x = 2 sin θ
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