Lesson 7.3 (1)

# Lesson 7.3 (1) - Volumes of Revolution The Shell Method...

This preview shows pages 1–11. Sign up to view the full content.

Volumes of Revolution The Shell Method Lesson 7.3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 Shell Method Based on finding volume of cylindrical shells Add these volumes to get the total volume Dimensions of the shell Radius of the shell Thickness of the shell Height
3 The Shell Consider the shell as one of many of a solid of revolution The volume of the solid made of the sum of the shells f(x) g(x) x f(x) – g(x) dx [ ] 2 ( ) ( ) b a V x f x g x dx π = -

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
4 Try It Out! Consider the region bounded by x = 0, y = 0, and 2 8 y x = - 2 2 2 0 2 8 V x x dx π = -
5 Hints for Shell Method Sketch the graph over the limits of integration Draw a typical shell parallel to the axis of revolution Determine radius, height, thickness of shell Volume of typical shell Use integration formula 2 radius height thickness π ⋅ ⋅ 2 b a Volume radius height thickness = ⋅

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
6 Rotation About x-Axis Rotate the region bounded by y = 4x and y = x 2 about the x-axis What are the dimensions needed? radius

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 09/13/2011 for the course CH 301 taught by Professor Fakhreddine/lyon during the Fall '07 term at University of Texas at Austin.

### Page1 / 11

Lesson 7.3 (1) - Volumes of Revolution The Shell Method...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online