In this video I go over question 3 on the Discovery Project: Rotating on a Slant video series. This time I derive the general formula for the volume of a shape generated by rotating a curve about a slanted line. I use the derivation I made earlier in Question 1 for the area of the region between the curve and the slanted line to solve for the volume. The volume equation I derive is very similar to that for the area but involves squaring the radius of revolution. To understand this question in detail, make sure to watch the first questions of this video series!
Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104360&authkey=!ABktqgP4-ovLXSE&ithint=file%2cpdf
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-discovery-project-rotating-on-a-slant-question-3
Related Videos:
Discovery Project: Rotating on a Slant: Question 3:
Discovery Project: Rotating on a Slant: Question 1:
Discovery Project: Patterns in Integrals: Question 1: 1/((x+a)(x+b)):
Discovery Project: Patterns in Integrals: Question 2: sin(ax)cos(bx):
Discovery Project: Patterns in Integrals: Question 3: x^n * ln(x):
Discovery Project: Patterns in Integrals: Question 4: x^n * e^6:
Area Under a Curve: Introduction to Integral Calculus:
Integrals and Volumes: .
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I don't always derive the volume of a shape rotated on a slanted line but when I do I usually need to make use of my earlier derivation on the area between a curve and a slanted line ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-discovery-project-rotating-on-a-slant-question-3