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anonymous
 5 years ago
Let R be the region enclosed by the graph of y=ln x, the line x=3, and the xaxis. (a) Fine the area of region R. (b) Find the volume of the solid generated by revolving region R about the xaxis. (c) Set up, but do not integrate, an integral expression in terms of a single variable for the volume of the solid generated by revolving region R about the line x=3.
anonymous
 5 years ago
Let R be the region enclosed by the graph of y=ln x, the line x=3, and the xaxis. (a) Fine the area of region R. (b) Find the volume of the solid generated by revolving region R about the xaxis. (c) Set up, but do not integrate, an integral expression in terms of a single variable for the volume of the solid generated by revolving region R about the line x=3.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok so you firstly have to integrate lnx to find the answer to the first question between 0 and 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you know how to do this??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I thought it would be from 1 to 3 because of the xaxis bound. The graph crosses the xaxis at (1,0).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So I took the integral of lnx and I got an answer of 1.296 after plugging in my bounds. I think this was the answer to part (a). Where I get confused is at part (b). I believe I have to integrate (lnx)² dx and multiply by pi. I got stuck at that step. How do you integrate that?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what was your general integral?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0In part (a) I used S lnx dx from [1,3] and in part (b) I'm using (pi) S (lnx)² dx from [1,3]. (S meaning integral)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0S for integral, there are no 5's

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yh i don't know how you got 1.296 tho

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for part b, try integration by parts to compute \[\int\limits_{1}^{3}\]pi*(lnx)^2dx

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Well, I integrated S lnx dx, and I got xlnxx. Then I plugged in my bounds [1,3]. So I got (3ln33)(ln11).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0part a is 1.296 your right about it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah, one of my friends told me to use integration by parts, but I don't remember how to do it... :P

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yh sorry .. i'm out of it .. trying 2 do too many things at once . i'm gonna sign out come bck on later .. sorrry for the confusion

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay! Thanks helping :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well u= lnx, du= dx/x, dv= lnx, so v= xlnx x and int(udv) = uv int(vdu)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that gives us lnx( xlnx x)  (xlnx2x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay, I think I'm following

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So in the way that you set up the u,du and v,dv, is it like setting it up (lnx)(lnx) with one being u and the other being dv?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If we're using the formula uv  int v du, then wouldn't it be lnx (xlnxx)  int xlnx x (1/x) dx?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ai, are you still there?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry was posting at another place ...yes! then divide (xlnxx)/x and get "lnx1" integrate it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay, I got lnx(xlnxx)xlnx+2x +c [1,3]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Alright! I got the answer :) it's 1.029 pi, or 3.233 if you multiply pi in. Do you know how to do part (c)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I know that in order to revolve the function about x=3, we must subtract 3 from our equation. I don't really understand how to set it up though.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0my replies are not going through :\ int(4e^y) over the region ..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Could you explain that for me? I don't really understand how you got that.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0correction : int(3e^y) ! well we have to rotate it around yaxis now i.e.at x=3..so write the function in terms of y, by that we get x= e^y.... the radius of rotation, if you visualize it would be 4f(y).......... PS the answer in reality doesn't makes sense as the given function on rotating on x=3 would overlap itself :\

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0why is it 3e^y? I understand how you switched from in terms of x to in terms of y x=e^y. but I'm confused again after that :S

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0can someone plx explain part c?
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