Using U-substitution to find the anti-derivative of a function. Seeing that U-substitution is the inverse of the chain rule.
Manipulating the expression to make u-substitution a little more obvious.
Using u-substitution and "back substituting" for x to simplify an expression
Another example of using U-subsitution
Doing u-substitution with ln(x)
Showing that, unlike line integrals of scalar fields, line integrals over vector fields are path direction dependent
Different ways of representing a flux integral
Concrete example of the derivative of a vector valued function to better understand what it means
Using Wolfram Alpha to approximate sin(x)
Visualizing Taylor Series for e^x
Washer method when rotating around a horizontal line that is not the x-axis
Setting up the definite integral for the volume of a solid of revolution around a vertical line using the "washer" or "ring" method.
These open-source mathematics homework problems are programmed for the WeBWorK mathematics platform and correspond to chapters in OpenStax Calculus Volume I. They were created through a Round Eight Textbook Transformation Grant.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Where a function is not differentiable.
Intuition as to why we go no net flux in the last worked example