This video looks at the Trapezoidal approximation of area under curve.
- Author:
- Khan, Salman
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This video looks at the Trig substitution with tangent.
- Author:
- Khan, Salman
This video looks at the Trig and u substitution together (part 1).
- Author:
- Khan, Salman
This video looks at the Trig and u substitution together (part 2).
- Author:
- Khan, Salman
This 11-minute video lesson provides an introduction to the triple integral.
- Author:
- Khan, Salman
This 8-minute video lesson looks at how to use a triple integral to find the mass of a volume of variable density.
- Author:
- Khan, Salman
This 12-minute video lesson demonstrates how to figure out the boundaries of integration.
- Author:
- Khan, Salman
This tutorial classifies regions in three dimensions. Comes in useful for some types of double integrals and we use these ideas to prove the divergence theorem.
- Author:
- Khan, Salman
This video looks at the definition and intuition for Type 2 Regions.
- Author:
- Khan, Salman
This video looks at the definition and intuition for type 3 regions.
- Author:
- Khan, Salman
U-substitution is a must-have tool for any integrating arsenal (tools aren't normally put in arsenals, but that sounds better than toolkit). It is essentially the reverise chain rule. U-substitution is very useful for any integral where an expression is of the form g(f(x))f'(x)(and a few other cases). Over time, you'll be able to do these in your head without necessarily even explicitly substituting. Why the letter "u"? Well, it could have been anything, but this is the convention. I guess why not the letter "u" :)
- Author:
- Khan, Salman
This video looks at another example of using u-subsitution.
- Author:
- Khan, Salman
This video looks at manipulating the expression to make u-substitution a little more obvious.
- Author:
- Khan, Salman
This video looks at using u-substitution and "back substituting" for x to simplify an expression.
- Author:
- Khan, Salman
This video covers example of using u-substitution to evaluate a definite integral.
- Author:
- Khan, Salman
This video covers doing u-substitution with ln(x).
- Author:
- Khan, Salman
This 12-minute video gives an example of using a line integral to find the work done by a vector field.
- Author:
- Khan, Salman
This video looks at using the product rule and the chain rule.
- Author:
- Khan, Salman
This 16-minute video lesson shows that unlike line integrals of scalar fields, line integrals over vector fields are path direction dependent.
- Author:
- Khan, Salman
This video looks at different ways of representing a flux integral.
- Author:
- Khan, Salman