This is an example of how to do a partial fractions decomposition when you're dealing with distinct quadratic factors.

Partial fractions, or partial fractions decomposition, is a way to evaluate integrals of rational functions. There are four types of factors you need to deal with when you're working through a partial fractions decomposition: Distinct linear factors Repeated linear factors Distinct quadratic factors Repeated quadratic factors You may also have a combination of these types of factors. This video is an example of how to use partial fractions when you're dealing with distinct linear factors.

Partial fractions, or partial fractions decomposition, is a way to evaluate integrals of rational functions. There are four types of factors you need to deal with when you're working through a partial fractions decomposition: Distinct linear factors Repeated linear factors Distinct quadratic factors Repeated quadratic factors You may also have a combination of these types of factors. This video is an example of how to use partial fractions when you're dealing with distinct linear factors.

Tabular integration is an alternative method to integration by parts, most commonly used when part of the function you're trying to integrate is a power function. Since tabular integration can't always be used, where integration by parts can, this method isn't usually taught.

When you use substitution in definite integrals, you have two options for dealing with the limits of integration. When you make the substitution, change the limits of integration so that they're associated with the substitution variable, instead of with the original variable. If you do this, you'll be able to plug the new limits of integration directly into the integrated function. When you make the substitution, leave the limits of integration in terms of the original variable. If you do this, you'll have to back-substitute to get the integration in terms of the original variable before evaluating over the limits of integration.

Part 2 of the Fundamental Theorem of Calculus defines the integral as the area under the curve.

The Fundamental Theorem of Calculus is the theorem that relates the derivative to the integral.

When you're asked to find area under the graph, you need to find net area. On the other hand, when you're asked to find area enclosed by the graph, you need to find gross area.

Simpson's rule, like Riemann sums and trapezoidal rule, is a method you can use to approximate the area under a curve.

Trapezoidal rule, like Riemann sums and Simpson's rule, is a method you can use to approximate the area under the curve. Trapezoidal rule can be more accurate than the other methods, because it uses trapezoids to get close to the curve, instead of rectangles.