Posts tagged integration applications
How to find the centroid of a plane region

The centroid of a plane region is the center point of the region over the interval [a,b]. In order to calculate the coordinates of the centroid, we’ll need to calculate the area of the region first. Then we can use the area in order to find the x- and y-coordinates where the centroid is located.

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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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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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