Like people, mathematical relations are not always explicit about their intentions. In this tutorial, we'll be able to take the derivative of one variable with respect to another even when they are implicitly defined (like "x^2 + y^2 = 1").
This video looks at the improper integral with two infinite bounds.
This video looks at the indefinite integrals of x raised to a power.
This series of videos focusing on calculus covers indefinite integral as anti-derivative, definite integral as area under a curve, integration by parts, u-substitution, trig substitution.
This video covers inflection points.
This video covers integral of ln x.
This 8-minute video lessons gives an example of using trig substitution to solve an indefinite integral.
This 8-minute video lesson looks at another example of finding an anti-derivative using trigonometric substitution.
This 18-minute video lesson shows an example using trig substitution (and trig identities) to solve an integral.
This video looks at the integration by parts twice for antiderivative of (x^2)(e^x).
This video looks at the integration by parts of (e^x)(cos x).
This 9-minute video lesson demonstrates how to use the definite integral to solve for the area under a curve. It also provides intuition on why the antiderivative is the same thing as the area under a curve.
Not everything (or everyone) should or could be proper all the time. Same is true for definite integrals. In this tutorial, we'll look at improper integrals--ones where one or both bounds are at infinity! Mind blowing!
This 9-minute video lesson provides an introduction to L'Hopital's Rule. [Calculus playlist: Lesson 36 of 156]
This 9-minute video lesson provides an introduction to L'Hopital's Rule. [Calculus playlist: Lesson 36 of 156]
Limits have done their part helping to find derivatives. Now, under the guidance of l'Hopital's rule, derivatives are looking to show their gratitude by helping to find limits. Ever try to evaluate a function at a point and get 0/0 or infinity/infinity? Well, that's a big clue that l'Hopital's rule can help you find the limit of the function at that point.
This 12-minute video lesson provides an introduction to limits.
This 19-minute video lesson provides an introduction to parametrizing a surface with two parameters.
We will now do another substitution technique (the other was u-substitution) where we substitute variables with trig functions. This allows us to leverage some trigonometric identities to simplify the expression into one that it is easier to take the anti-derivative of.
This 19-minute video lesson provides an Introduction to the Line Integral.