Trigonometric Integrals and Substitutions
Interactive Video
•
Mathematics
•
11th Grade - University
•
Practice Problem
•
Hard
+2
Standards-aligned
Amelia Wright
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What should you do if the power of sine is odd in a trigonometric integral?
Use double-angle identities.
Use half-angle identities.
Save one factor of cosine and convert the rest to sines.
Save one factor of sine and convert the rest to cosines.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the first example, what substitution is made after rewriting the integral?
u = sine 2x
u = cosine 2x
u = secant 2x
u = tangent 2x
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What identity is used to rewrite cosine to the fourth power in the first example?
secant squared x = 1 + tangent squared x
cosine squared x = 1 - sine squared x
sine squared x = 1 - cosine squared x
tangent squared x = secant squared x - 1
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the second example, what is the substitution made for the variable u?
u = secant x
u = tangent x
u = cosine x
u = sine x
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the differential du equal to in the second example?
negative cosine x dx
sine x dx
cosine x dx
negative sine x dx
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the expression simplified before integration in the second example?
By completing the square
By expressing in terms of u to the negative powers
By using partial fractions
By factoring out a common term
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of evaluating the definite integral at the upper limit in the second example?
Pi
Square root of three
One
Zero
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