Posts tagged integration
Surface area of revolution around the x-axis and y-axis

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.

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U-substitution to solve definite integrals

U-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.

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Theorem of Pappus to find volume using the centroid

The 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.

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Probability density functions and probability of X in an interval

Probability 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].

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Work done on elastic springs, and Hooke's law

To 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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