We can use integrals to find the surface area of the three-dimensional figure that’s created when we take a function and rotate it around an axis and over a certain interval. The formulas we use to find surface area of revolution are different depending on the form of the original function and the axis of rotation.

Read MoreSometimes we’ll be asked for the radius and interval of convergence of a Taylor series. In order to find these things, we’ll first have to find a power series representation for the Taylor series.

Read MoreU-substitution in definite integrals is just like substitution in indefinite integrals except that, since the variable is changed, the limits of integration must be changed as well. If you don’t change the limits of integration, then you’ll need to back-substitute for the original variable at the end.

Read MoreThe comparison test for convergence lets us determine the convergence or divergence of the given series by *comparing* it to a similar, but simpler comparison series. We’re usually trying to find a comparison series that’s a geometric or p-series, since it’s very easy to determine the convergence of a geometric or p-series.

Any point in the coordinate plane can be expressed in both rectangular coordinates and polar coordinates. Instead of moving out from the origin using horizontal and vertical lines, like we would with rectangular coordinates, in polar coordinates we instead pick the angle, which is the direction, and then move out from the origin a certain distance.

Read MoreThe Theorem of Pappus tells us that the volume of a three-dimensional solid object that’s created by rotating a two-dimensional shape around an axis is given by V=Ad. V is the volume of the three-dimensional object, A is the area of the two-dimensional figure being revolved, and d is the distance traveled by the centroid of the two-dimensional figure.

Read MoreThe alternating series estimation theorem gives us a way to approximate the sum of an alternating series with a remainder or error that we can calculate. To use the theorem, the alternating series must follow two rules.

Read MoreProbability density refers to the probability that a continuous random variable X will exist within a set of conditions. It follows that using the probability density equations will tell us the likelihood of an X existing in the interval [a,b].

Read MoreSometimes it’s easy to forget that there’s a difference between the *limit* of an infinite series and the *sum* of an infinite series. They’re two very different things, and we use a different calculation to find each one.

Before we can learn how to determine the convergence or divergence of a geometric series, we have to define a geometric series. Once you determine that you’re working with a geometric series, you can use the geometric series test to determine the convergence or divergence of the series.

Read MoreTo find the work required to empty a tank, first divide the tank into an infinite number of slices, then calculate the work required to remove a single slice of substance from the tank, then develop an equation to solve for the work needed to empty the entire tank, based on the work that was required to remove the single slice.

Read MoreOne convenient way to find the sum of the Maclaurin series is to start with a well-known Maclaurin series and then manipulate it one step at a time until it matches the series you’ve been given. Because you’ll be manipulating the expression of the sum at the same time, once you get the series to match, you’ll automatically have the sum.

Read MoreTo find the work required to stretch or compress an elastic spring, you’ll need to use Hooke’s Law. Every spring has its own spring constant k, and this spring constant is used in the Hooke’s Law formula.

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