Calc07_4day2 - y-axis. 3 4 dx dy = -15 = s . . S A rs = 3 5...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
7.4 Day 2 Surface Area Greg Kelly, Hanford High School, Richland, Washington (Photo not taken by Vickie Kelly)
Background image of page 1

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

View Full DocumentRight Arrow Icon
Surface Area: ds r Consider a curve rotated about the x -axis: The surface area of this band is: 2 r ds π⋅ The radius is the y -value of the function, so the whole area is given by: 2 b a y ds π This is the same ds that we had in the “length of curve” formula, so the formula becomes: Surface Area about x -axis (Cartesian): 2 2 1 b a dy S y dx dx = + To rotate about the y -axis, just reverse x and y in the formula!
Background image of page 2
4 4 3 y x = - + Example: Rotate about the y -axis. 4 4 3 y x - = - 3 3 4 y x - + = 3 3 4 x y = - + 3 4 dx dy = -
Background image of page 3

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

View Full DocumentRight Arrow Icon
Example: Rotate about the y -axis. 3 4 dx dy = - 2 4 0 3 3 2 3 1 4 4 S y dy π = - + + 4 0 3 25 2 3 4 16 y dy = - + 4 0 3 5 2 3 4 4 y dy = - + 4 2 0 5 3 3 2 8 y y = - + [ ] 5 6 12 2 = - + 5 6 2 = 15 = 3 3 4 x y = - +
Background image of page 4
4 4 3 y x = - + Example: Rotate about the
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

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

View Full DocumentRight Arrow Icon
Background image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y-axis. 3 4 dx dy = -15 = s . . S A rs = 3 5 = 15 = From geometry: Example: y x = rotated about x-axis. 2 9 2 1 dy S y dx dx = + 2 ( (1 ( , ) ^ 2), ,0,9) y d y x x + 117.319 ENTER ( ) x ENTER Y STO Example: 2 2 1 y x = -2 1 y x =-12.5663706144 Check: rotated about x-axis. 2 2 1 x y + = 2 1 1 2 1 dy S y dx dx - = + 2 ( (1 ( , ) ^ 2), , 1,1) y d y x x +- 2 . . 4 S A r = 4 = 12.5663706144 ENTER (1 ^ 2) x-ENTER Y STO Dont forget to clear the x and y variables when you are done! ENTER F4 4 , Y X Once again...
View Full Document

Page1 / 8

Calc07_4day2 - y-axis. 3 4 dx dy = -15 = s . . S A rs = 3 5...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online