Instructional Video
Sophia Learning

Sophia: Volume Integrals: Lesson 3

9th - 10th
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."
Instructional Video
Sophia Learning

Sophia: Volume Integrals: Lesson 5

9th - 10th
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."
Instructional Video
Sophia Learning

Sophia: Modified Limits of Integral: Lesson 2

9th - 10th
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."
Instructional Video
Sophia Learning

Sophia: Modified Limits of Integral: Lesson 4

9th - 10th
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."
Instructional Video
Sophia Learning

Sophia: Second Fundamental Theorem of Calculus: Lesson 4

9th - 10th
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."
Instructional Video
Sophia Learning

Sophia: Using the Derivative of Natural Log in Integrals: Lesson 2

9th - 10th
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."