How to Calculate Volume of Solids With Known Cross Sections (Calculus 2 Lesson 5)

In this video we look at how to use definite integrals to calculate the volume of solids with known cross sections, such as squares, rectangles, semicircles, and triangles (also known as volume by slicing). We look at the area formulas for each type of cross section, and look at example problems of calculating the volume of solids that have these cross sections either perpendicular to the x-axis or y-axis.

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This series is designed to help students understand the concepts of Calculus 2 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!

Calculus 2 requires a solid understanding of calculus 1, precalculus, and algebra concepts and techniques. This includes limits, differentiation, basic integration, factoring, equation manipulation, trigonometric functions, logarithms, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!


Video Chapters:
0:00 Definite Integrals for Volume With Known Cross Sections
2:09 Examples of Solids With Known Cross Sections
5:24 Common Cross Sections & Area Formulas
7:08 Example 1 - y=sqrt(x), x=9, y=0, Squares Perpendicular to x-axis
11:47 Example 2 - y=x/2, y=2, x=0, Semicircles Perpendicular to y-axis
18:25 Example 3 - y=4-x, y=x-1, x=0, Equilateral Triangles Perpendicular to x-axis
30:00 Outro


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