anonymous
  • anonymous
the region enclosed by the graphs of y=e^(x/2), y=1, and x=ln3 is revolved about the x-axis. Find the volume of the solid generated??????? I NEED CALCULUS HELP PLEASE
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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amistre64
  • amistre64
yay!! an easy one
anonymous
  • anonymous
easy? lol i would love your help then :)
amistre64
  • amistre64
lets see where these curves meet; and what our boundaries are

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amistre64
  • amistre64
e^(x/2) = 1 when x=0 right?
anonymous
  • anonymous
yes
amistre64
  • amistre64
x = ln(3) is just a constant; we can find it on a calculator
anonymous
  • anonymous
yea 1.098
amistre64
  • amistre64
right; 1.09861...
amistre64
  • amistre64
let me draw a pic of my interpretation of the bonds then
anonymous
  • anonymous
i think they intersect at 0 and ln3 but i dont know how to integrate it
amistre64
  • amistre64
like this?
1 Attachment
amistre64
  • amistre64
theres only two things to integrate here; from 0 to ln(3) right?
anonymous
  • anonymous
yes
amistre64
  • amistre64
lets find the volume of the top curve; then we will cut out the section below y=1ok
anonymous
  • anonymous
yes that would work but im suppose to do something with (pie)
amistre64
  • amistre64
pi {S} [e^(1/2(x))]^2 dx ; [0,ln(3)]
amistre64
  • amistre64
what is e^(x/2)^2 =? e^x right?
anonymous
  • anonymous
yes because they would cancel
amistre64
  • amistre64
the key here is to realize that we are adding up all the areas of circles that have been sliced; the area of a circle = pi r^r it just so happens the r = f(x)
amistre64
  • amistre64
r^2 that is lol
amistre64
  • amistre64
so; [f(x)]^2 = e^(x/2)^2 = e^x pi {S} e^x dx ; [0,ln(3)] whats the integral of e^x?
anonymous
  • anonymous
the antiderivetive? its justs e^x
amistre64
  • amistre64
e^x is its own derivative; so its its own integral :) yes
amistre64
  • amistre64
pi [ e^(ln(3)) e^(0) ] = ?
amistre64
  • amistre64
typoed that
amistre64
  • amistre64
pi [ e^(ln(3)) - e^(0) ] = ?
anonymous
  • anonymous
an example my teacher did shows it being {S} (pi (e^x)-1) and then taking the antiderivetive of that
amistre64
  • amistre64
lets stay on one track here; well jump the track when we get to the end
anonymous
  • anonymous
ok i understand that i just dont understand where the minus 1 came from?
amistre64
  • amistre64
right now we are making a solid piece; we will then cut out the senter
amistre64
  • amistre64
pi [e^(ln3) - e^0] = ??
anonymous
  • anonymous
o so we r taking the whole volume minus the part we dont need which is the y=1
amistre64
  • amistre64
exaclty :) we can do it in parts or all togther; makes no difference
anonymous
  • anonymous
gotcha and i got 2 for that answer
amistre64
  • amistre64
2 or 2pi?
anonymous
  • anonymous
2 pi
amistre64
  • amistre64
good :) now let integrate y = 1 from 0 to ln(3); or do you know a shortcut for this one?
amistre64
  • amistre64
pi {S} 1 dx ; [0,ln3] becomes?
anonymous
  • anonymous
pi (x)= pi (ln3)
amistre64
  • amistre64
good :) 2pi - ln(3) pi is your answer then
amistre64
  • amistre64
pi [ 2 - ln(3)] even lol
anonymous
  • anonymous
and that is what the back of the book says...you are good lol
amistre64
  • amistre64
toldja it was easy lol
amistre64
  • amistre64
adding up areas of circles; thats all
anonymous
  • anonymous
yea i just suck at it when my teacher tries to explain it..i may need more help in a few
amistre64
  • amistre64
im sure well be around
anonymous
  • anonymous
ok thank you :)
anonymous
  • anonymous
u still there? i have a quick question?

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