
Understanding Anti-Derivatives and Substitution

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned

Ethan Morris
FREE Resource
Standards-aligned
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8 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the initial function for which we are trying to find the anti-derivative?
R cos x raised to the power of 3 divided by the square root of 1 - x^2
R sin x raised to the power of 3 divided by the square root of 1 - x^2
R cos x raised to the power of 2 divided by the square root of 1 - x^2
R sin x raised to the power of 2 divided by the square root of 1 - x^2
Tags
CCSS.HSF.TF.C.8
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the derivative of R sin x?
1 / the square root of x^2 - 1
1 / the square root of x^2 + 1
1 / the square root of 1 - x^2
1 / the square root of 1 + x^2
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What substitution is made to simplify the integral?
Let U equal R cos x
Let U equal R sin x
Let U equal R tan x
Let U equal R cot x
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
After substitution, what does the integral become in terms of U?
Integral of U to the fourth du
Integral of U squared du
Integral of U to the fifth du
Integral of U cubed du
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the anti-derivative of U squared in terms of U?
U to the fifth divided by 5 plus C
U to the fourth divided by 4 plus C
U squared divided by 2 plus C
U cubed divided by 3 plus C
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the final anti-derivative in terms of x?
R sin x squared divided by 2 plus C
R sin x to the fifth divided by 5 plus C
R sin x cubed divided by 3 plus C
R sin x to the fourth divided by 4 plus C
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the anti-derivative function represent?
The derivative of this function is equal to zero
The derivative of this function is equal to infinity
The derivative of this function is equal to a constant
The derivative of this function is equal to the original integrand
8.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of finding the anti-derivative in terms of x?
To express the solution in the original variable
To simplify the equation
To eliminate the constant of integration
To find the maximum value of the function
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