Why is it important to apply variable substitution in trigonometric integrals?

Trigonometric Integrals and Derivatives

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Mathematics
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10th - 12th Grade
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Hard

Lucas Foster
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
To make the integral more complex.
To change the variable of integration.
To avoid using trigonometric functions.
To simplify the integral and make it comparable to known formulas.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the first example, what is the argument of the sine function?
7y
cosine
y
7
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of 7y with respect to y?
0
1
7
y
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why do we introduce and then divide by 7 in the integral?
To avoid using trigonometric functions.
To change the variable of integration.
To make the integral more complex.
To ensure the integral remains unchanged.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the integral of sine(B) with respect to B?
-sin(B) + C
sin(B) + C
cos(B) + C
-cos(B) + C
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
After integrating, what should be done to revert to the original variable?
Multiply by the original variable.
Change the variable again.
Substitute back the original variable.
Differentiate the result.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the final form of the integral in the first example?
cos(7y) + C
-cos(7y) + C
-sin(7y) + C
sin(7y) + C
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