Category: Definite integrals

Learn how to easily calculate the volume of a solid of revolution using a simple formula from elementary school. Discover the method through an example of calculating the volume of a sphere formed by rotating a curve around an axis, without complex integrals.

Definite integrals can be calculated with respect to variable x or y, and sometimes should be, if it’s more convenient. This often plays a big role in the applications of integrals, such as calculating the areas of regions, arc lengths, volumes, and surface areas of solids of revolution. Often we don’t even have a choice, because the conditions of the problem specify that the curve rotates around the OY axis, not the OX. How do you do that?

Discover how to effectively change integration limits by substitution in definite integral tasks. This article explains in detail the step-by-step process of changing limits, using real examples and formulas to simplify understanding of this crucial mathematical technique.