This 9-minute video lesson uses the disk method around the y-axis.
This 10-minute video lesson provides an introduction to the divergence of a vector field.
This 11-minute video lecture examines the intuition of what the divergence of a vector field is.
This 11-minute video lecture analyzes a vector field using its divergence.
This video looks at the example of calculating the flux across a surface by using the divergence Theorem.
You know what the divergence theorem is, you can apply it and you conceptually understand it. This tutorial will actually prove it to you (references types of regions which are covered in the "types of regions in 3d" tutorial.
This video looks at breaking up the surface integral.
evaluating the surface integral.
This video covers more evaluation of the surface integral.
This video looks at Home stretch. Proving the Type i part.
This video looks at the divergent improper integral.
This video looks at the example where we do substitution twice to get the integral into a reasonable form.
This 10-minute video lecture provides an Introduction to the double integral.
This 10-minute video lesson on double integrals demonstrates how to Figure out the volume under z=xy^2.
This 8-minute video lesson on double integrals demonstrates how to integrate dy first!
This 9-minute video lesson demonstrates another way to conceptualize the double integral.
This 10-minute video lesson on double integrals shows how to find the volume when we have variable boundaries.
This 10-minute video lesson shows how to evaluate the double integrals with y=x^2 as one of the boundaries.
A single definite integral can be used to find the area under a curve. with double integrals, we can start thinking about the volume under a surface!
This is about as many integrals we can use before our brains explode. Now we can sum variable quantities in three-dimensions (what is the mass of a 3-D wacky object that has variable mass)!