Homework Soursehi I need help with a washer method problem chapter 62 probl
hi, I need help with a washer method problem, chapter 6.2 problem #16 in the 7th edition.
The instructions say to graph it and find the volume of the solid, I think I have the correct graph, I just don\'t know how to go about finding the volume.
Here is the equation:
xy=1, y=0, x=1, x=2; about x=-1
Thanks in advance!
The instructions say to graph it and find the volume of the solid, I think I have the correct graph, I just don\'t know how to go about finding the volume.
Here is the equation:
xy=1, y=0, x=1, x=2; about x=-1
Thanks in advance!
Solution
This triangle has boundary lines (1, 1) to (2, 2): y = x (1, 1) to (1, 2): x = 1 (1, 2) to (2, 2): y = 2. So, we are revolving the region bounded between the lines y = x and y = 2 for x in [1, 2] about the line x = 10/3 (which is parallel to the y-axis). Taking a vertical strip at x in [1, 2], rotating this about x = 10/3 yields a cylindrical shell with radius (10/3 - x) via \"right - left\" and height (2 - x) via \"top - bottom\". (Sketch this!) So, using cylindrical shells yields ?(x = 1 to 2) 2p (10/3 - x)(2 - x) dx = ?(x = 1 to 2) 2p (x^2 - 16x/3 + 20/3) dx = 2p (x^3/3 - 8x^2/3 + 20x/3) {for x = 1 to 2} = (2p/3) (x^3 - 8x^2 + 20x) {for x = 1 to 2} = (2p/3) [(8 - 32 + 40) - (1 - 8 + 20)] = 2p.
