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Sophia Learning
Sophia: Matching Limits and Differential: Lesson 5
This lesson explains that the limits of integration must be kept in terms of the differential. It is 5 of 5 in the series titled "Matching Limits and Differential."
Sophia Learning
Sophia: Modified Limits of Integral: Lesson 3
This lesson introduces the possibility of changing the scale of definite integration to expedite the process. It is 3 of 4 in the series titled "Modified Limits of Integral."
Sophia Learning
Sophia: Reverse Chain Rule: Lesson 2
The concept of applying the chain rule in reverse when finding an anti-derivative is discussed here. This lesson is 2 of 6 in the series titled "Reverse Chain Rule."
Sophia Learning
Sophia: Reverse Chain Rule: Lesson 4
The concept of applying the chain rule in reverse when finding an anti-derivative is discussed here. This lesson is 4 of 6 in the series titled "Reverse Chain Rule."
Sophia Learning
Sophia: Reverse Chain Rule: Lesson 6
The concept of applying the chain rule in reverse when finding an anti-derivative is discussed here. This lesson is 6 of 6 in the series titled "Reverse Chain Rule."
Sophia Learning
Sophia: Second Fundamental Theorem of Calculus: Lesson 2
The process of applying the limits of integration for a definite integral is introduced here. This lesson is 2 of 5 in the series titled "Second Fundamental Theorem of Calculus."
Sophia Learning
Sophia: Using Integration in Many Ways
This lesson practices using integration to solve problems not involving time or spatial parameters.
Sophia Learning
Sophia: Using Integration in Many Ways
This lesson practices using integration to solve problems not involving time or spatial parameters.
Sophia Learning
Sophia: Using Integration in Many Ways: Lesson 5
This lesson practices using integration to solve problems not involving time or spatial parameters. It is 5 of 5 in the series titled "Using Integration in Many Ways."
Sophia Learning
Sophia: Using the Derivative of Natural Log in Integrals: Lesson 6
This lesson practices rewriting the integrand as the derivative of a function over the function in order to simplify integration. It is 6 of 7 in the series titled "Using the Derivative of Natural Log in Integrals."
Sophia Learning
Sophia: Using the Derivative of Natural Log in Integrals: Lesson 7
This lesson practices rewriting the integrand as the derivative of a function over the function in order to simplify integration. It is 7 of 7 in the series titled "Using the Derivative of Natural Log in Integrals."
Sophia Learning
Sophia: Volume Integrals: Lesson 2
The idea that integration can be used to determine a volume is discussed here. This lesson is 2 of 5 in the series titled "Volume Integrals."
Sophia Learning
Sophia: Volume Integrals: Lesson 3
The idea that integration can be used to determine a volume is discussed here. This lesson is 3 of 5 in the series titled "Volume Integrals."
Sophia Learning
Sophia: Volume Integrals: Lesson 5
The idea that integration can be used to determine a volume is discussed here. This lesson is 5 of 5 in the series titled "Volume Integrals."
Sophia Learning
Sophia: Modified Limits of Integral: Lesson 2
This lesson introduces the possibility of changing the scale of definite integration to expedite the process. It is 2 of 4 in the series titled "Modified Limits of Integral."
Sophia Learning
Sophia: Modified Limits of Integral: Lesson 4
This lesson introduces the possibility of changing the scale of definite integration to expedite the process. It is 4 of 4 in the series titled "Modified Limits of Integral."
Sophia Learning
Sophia: Second Fundamental Theorem of Calculus: Lesson 4
The process of applying the limits of integration for a definite integral is introduced here. This lesson is 4 of 5 in the series titled "Second Fundamental Theorem of Calculus."
Sophia Learning
Sophia: Using the Derivative of Natural Log in Integrals: Lesson 2
This lesson practices rewriting the integrand as the derivative of a function over the function in order to simplify integration. It is 2 of 7 in the series titled "Using the Derivative of Natural Log in Integrals."