Volume Using Known Cross Sections (Slicing) | Calculus 2 Lesson 5 - JK Math

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. 🖥️ Join My Membership Site: https://www.jkmathematics.com/plus 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 📝 Examples Video:    • Volume Using Known Cross Sections (Slicing...   ⏩ Next Lesson:    • Arc Length | Calculus 2 Lesson 6 - JK Math   📺 Calculus 2 Playlist:    • Calculus 2   📺 Calculus 1 Playlist:    • Calculus 1   🌐 Visit My Website: https://www.jkmathematics.com ⚡️Math Products I Recommend⚡️ Graphing Calculator: https://amzn.to/3XuUcB9 Non-Graphing Calculator: https://amzn.to/46hHJ7E Financial Calculator: https://amzn.to/3CRe9s4 Graphing Paper: https://amzn.to/46mAfAr College Rule Paper: https://amzn.to/3NOJaTN My Favorite Pencil: https://amzn.to/3NOFMIB My Favorite Erasers: https://amzn.to/3PumUQB Calculus Workbook: https://amzn.to/3r8SnNP ⚡️Textbooks I Use⚡️ Calculus 1 & 2: https://amzn.to/3PzfI5F Calculus 3: https://amzn.to/46rSy76 Financial Mathematics: https://amzn.to/3ppIVW0 ⚡️My Recording Equipment⚡️ iPad Air: https://amzn.to/3phEug1 Apple Pencil (Gen 2): https://amzn.to/3Nl45MM Tablet Desk Stand: https://amzn.to/4420rPh External Hardrive: https://amzn.to/44pkEyh (Commissions earned on qualifying purchases) Find me on social media: Facebook:   / jkmathematics   Twitter:   / jk_mathematics   Instagram: @jk_mathematics Found this video to be helpful? Consider giving this video a like and subscribing to the channel! Thanks for watching! Any questions? Feedback? Leave a comment! -Josh from JK Math #calculus Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.