Mathematics
OpenStudy (anonymous):

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer. y=x, y=0, x=2, and x=4; about x=1 I have nooo idea how to do this, the answers at the back of the textbook has 2 washers drawn, one at the top and the other at the bottom. I find this really complicated and I'm desperate for help :(

OpenStudy (anonymous):

i'm a bit puzzled about how this looks - do you have a drawing of the curves (lines)?

OpenStudy (anonymous):

yes jimmyrep, i will attach the file right now :)

OpenStudy (anonymous):

right

OpenStudy (anonymous):

OpenStudy (anonymous):

This is a simpler diagram of just the lines, without the actual picture of the solid.

OpenStudy (anonymous):

sorry i87 - i have to go out for a while be back in 1 hour if question is still open I'll look at it then

OpenStudy (anonymous):

no problem, thanks

OpenStudy (anonymous):

ok - have you done any calculus

OpenStudy (anonymous):

yes i have, not this type though, mine was introductory calculus

OpenStudy (anonymous):

integration?

OpenStudy (anonymous):

yes, iknow integration

OpenStudy (anonymous):

my main issue here was coming up with the diagram of the solid (diagram 1)

OpenStudy (anonymous):

like i was able to draw the graph, i just didnt know how the textbook ended up with a such a complex diagram

OpenStudy (anonymous):

right - the volume of rotation is the sum of all the tubes with very small thiskness formed on rotation. The thickness is dx and their length is the various values of y The general formula for integration of this is $2\pi \int\limits_{b}^{a} xy dx$

OpenStudy (anonymous):

In this case the curve ( line in this case) is y =x and the limits are 3 and 1 so we have INt 2pi x^2 dx = 2pi[ x^3/3} between 1 and 3 = 2pi [ 3^3 / 3 - 1^3 / 3] = 2pi * 26/3 = 52pi/3 i cubic units = 54.45 cu units

OpenStudy (anonymous):

ok, that makes sense :)

OpenStudy (anonymous):

i know you took a huge chunk of ur time to help me out and i really appreciate that

OpenStudy (anonymous):

hold on i87 - theres a mistake the integral is INT 2pi x(x+1) between 1 and 3 not as i said

OpenStudy (anonymous):

oh, alright, thanks for the correction.