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πΆUnit 8

1 min readβ’june 8, 2020

Anusha Tekumulla

The **disc method **is a way to find the volume by **rotating around the x- or y-axis**. In this situation, we will find the volume by adding up a bunch of infinitely thin **circles**.Β

Letβs look at the region between the curve y = βx and the x-axis from x = 0 and x = 1.Β

If you **rotate this region** around the x-axis, the **cross sections will be circles with radii βx**. Thus, the area of each cross section will be Ο(βx)^2 or Οx. Now we can **integrate **Οx from x = 0 and x = 1 to get the volume.Β

Now, letβs generalize this. If you have a region whose area is bounded by the curve y = f(x) and the x-axis on the interval [a,b], each disk has a radius of f(x), and the area of the disk will beΒ Β

To find the volume, **evaluate the integral.Β **

Now, you try to use the formula with this example problem:Β

If rotate the function y = x + 2 about the x-axis from x = 0 to x = 2, what is the volume of the figure?Β

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