Volume of solid under the curve y= 7/(x^2 +5x +6)  TOPIC_SOLVED

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Volume of solid under the curve y= 7/(x^2 +5x +6)

Postby chinex9a on Sat Oct 09, 2010 10:50 pm

I am studying for an exam and I don't you know how to go about this?

Volume of solid under the curve y= 7/(x^2 +5x +6) from x = 0 to x = 1 if rotated about the y-axis.

I made x the subject of the formula getting (sqrt(y+28)-5 sqrt(y))/(2 sqrt(y)) and then I found what y is when x= 0 and x=1, which were y=7/6 and y=7/12 respectively.

then I integrated using (pi*(f(y))^2*dy); pi*((sqrt(y+28)-5 sqrt(y))/(2 sqrt(y)))^2 to get the volume then I got

pi*(-7/12+105 log(2)-70 log(3)+log(128)) which is aprroximately 0.46.


I know the answer isn't correct because I checked the answers on my text book. Plz help me understand this problem

Thank you :)
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Re: Volume of solid under the curve y= 7/(x^2 +5x +6)

Postby Martingale on Sun Oct 10, 2010 3:10 am

chinex9a wrote:...

I made x the subject of the formula getting (sqrt(y+28)-5 sqrt(y))/(2 sqrt(y)) and then I found what y is when x= 0 and x=1, which were y=7/6 and y=7/12 respectively.
...


Why would you want to do that?
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Re: Volume of solid under the curve y= 7/(x^2 +5x +6)

Postby chinex9a on Sun Oct 10, 2010 3:23 am

because we are rotating about the y axis :confused:
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Re: Volume of solid under the curve y= 7/(x^2 +5x +6)

Postby Martingale on Sun Oct 10, 2010 4:29 am

chinex9a wrote:because we are rotating about the y axis :confused:


So. Use the method of cylindrical shells.
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Re: Volume of solid under the curve y= 7/(x^2 +5x +6)

Postby chinex9a on Sun Oct 10, 2010 4:41 am

Yes that is what I did right. pi*(f(y))^2 dy
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Re: Volume of solid under the curve y= 7/(x^2 +5x +6)

Postby Martingale on Sun Oct 10, 2010 5:02 am

chinex9a wrote:Yes that is what I did right. pi*(f(y))^2 dy


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Re: Volume of solid under the curve y= 7/(x^2 +5x +6)

Postby chinex9a on Sun Oct 10, 2010 5:13 am

and so are b and a 7/6 and 7/12 ?
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Re: Volume of solid under the curve y= 7/(x^2 +5x +6)

Postby chinex9a on Mon Oct 11, 2010 3:54 pm

Am I correct???????????? :?:
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Re: Volume of solid under the curve y= 7/(x^2 +5x +6)  TOPIC_SOLVED

Postby Martingale on Mon Oct 11, 2010 4:07 pm

chinex9a wrote:and so are b and a 7/6 and 7/12 ?


No. a and b are 0 and 1
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