What is the first step in using the method of substitution for evaluating a definite integral?

Antiderivatives and Integration Techniques

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Mathematics
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10th - 12th Grade
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Hard

Olivia Brooks
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Let part of the integrand be equal to u.
Factor out constants from the integrand.
Determine the limits of integration.
Find the antiderivative of the integrand.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When determining differential u, what is it equal to in this example?
1 divided by the square root of 1 minus x squared dx
Negative 1 divided by the square root of 1 minus x squared dx
Inverse cosine of x dx
x squared dx
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What should be considered when rewriting the integral with respect to u?
The limits of integration should be left off initially.
The integrand should be multiplied by a constant.
The original limits of integration should be used.
The differential should be ignored.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is one option when finding the antiderivative with respect to u?
Ignore the limits of integration.
Find the derivative instead.
Convert back to x and use original limits.
Use the same limits as x.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the lower limit of integration determined when x equals 0?
By setting u equal to x.
Using the unit circle to find the angle with cosine value 0.
By calculating the inverse sine of 0.
Using the derivative of the function.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the upper limit of integration when x equals 1/2?
Pi
Pi divided by 2
Pi divided by 3
Pi divided by 4
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the unit circle in this context?
It is used to factor the integrand.
It provides the value of the integral.
It is used to determine the limits of integration.
It helps find the derivative of the function.
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