In this video I go over an introduction in integrals and volumes and define the volume of a general shape using integrals. This is an extremely important concept in not only mathematics but also in science and technology as a whole as it allows for the ability to calculate exactly the volume of almost any shape.

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Integrals and Volumes

The volumes of some common shapes are shown below:

But what about general non-basic shapes?

Important Note: This definition does not depend on the shape's relative distance from the x or y-axis.

Consider the basic half-cylinder shape from above: