Hello again! Could someone suggest what method I should use to solve this question:
1) integral (0.1 > 0) x^2.e^x^3 dx
I tried using by parts twice but I got stuck the second time round as it didnt seem to have made the integral any easier. (i am right in thinking that integral of e^x^3 = [1/3x^2]e^x^3?)
Secondly, could someone work through the below problem as I end up with something completely different to the answers! arghh:
2) Find, in terms of e and pi, the volume generatre when the region bounded by the lines x=1, x=3 and y=0 and the curve with equation y=e^[3x/2] is rotated completely about the xaxis.
Thank you all so much  i figured you wouldn't mind too much as you'll enjoy the P3 practise ready for next week!
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Hoofbeat
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 01062004 12:40

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 01062004 12:45
(Original post by Hoofbeat)
2) Find, in terms of e and pi, the volume generatre when the region bounded by the lines x=1, x=3 and y=0 and the curve with equation y=e^[3x/2] is rotated completely about the xaxis.
Thank you all so much  i figured you wouldn't mind too much as you'll enjoy the P3 practise ready for next week! 
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 01062004 12:47
1. Spot that the derivative of x^3 = 3x^2 so use the substitution u=x^3, dx = du/(3x^2)
I don't think it's possible to integrate e^x^3  when you differentiate [1/3x^2]e^x^3 you'd need to use the quotient rule as well as the chain rule. 
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 01062004 12:48
(Original post by mockel)
For 2), I get V = (1/3)(pi)e³[ e³  1] ??? 
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 01062004 12:50
(Original post by Hoofbeat)
Hello again! Could someone suggest what method I should use to solve this question:
1) integral (0.1 > 0) x^2.e^x^3 dx
Edit: just saw your posts bezza.....glad to know that I seem to be hitting my peak just before the exam 
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 01062004 13:03
well integrating e^x^3 is ok since u can let u = x^3 and du/dx = 3x^2 therefore reaaraging gives 1/3du = x^2 dx.
so this means integrating 1/3e^u which is 1/3e^u (u = x^3) so this becomes 1/3e^x^3. sticking the limits in gives 1/3e^1/1000  1/3. put 1/3 outside into a bracket and becomes 1/3(e^0.001  1).
?? plizzz say dats ryt! 
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 01062004 13:06
(Original post by Jubba)
well integrating e^x^3 is ok since u can let u = x^3 and du/dx = 3x^2 therefore reaaraging gives 1/3du = x^2 dx.
so this means integrating 1/3e^u which is 1/3e^u (u = x^3) so this becomes 1/3e^x^3. sticking the limits in gives 1/3e^1/1000  1/3. put 1/3 outside into a bracket and becomes 1/3(e^0.001  1).
?? plizzz say dats ryt! 
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 01062004 13:13
(Original post by Hoofbeat)
Hello again! Could someone suggest what method I should use to solve this question:
1) integral (0.1 > 0) x^2.e^x^3 dx
I tried using by parts twice but I got stuck the second time round as it didnt seem to have made the integral any easier. (i am right in thinking that integral of e^x^3 = [1/3x^2]e^x^3?)
Secondly, could someone work through the below problem as I end up with something completely different to the answers! arghh:
2) Find, in terms of e and pi, the volume generatre when the region bounded by the lines x=1, x=3 and y=0 and the curve with equation y=e^[3x/2] is rotated completely about the xaxis.
Thank you all so much  i figured you wouldn't mind too much as you'll enjoy the P3 practise ready for next week!
the second one is basically integrate between 1 and 3, pi y^2 dx.
so it's the integral of pi e^3x = 1/3 pi e^3x, between limits 1 and 3. so your answer should be 1/3 pi (e^9  e^3).
i hope that's right 
SUKBarracuda
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 01062004 13:15
could someone work through the below problem
The volume of a rotated shape is the (pi) x ∫y² dx
This gives (pi) x ∫(e^(3x/2))^2 dx (Between limits 1 and 3)
= (pi) x ∫e^(3x) dx
= (pi)[(1/3)(e^3x)] between 1 and 3
Take out the factors 1/3 and e^3 gives::
(1/3)(pi)e³[ e^6  1]
I think bezza and mockel have accidently put e^3 in the brackets, but e^9 = e^3 x e^6, and not e^3 x e^3!
Hope this helps 
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 01062004 13:15
(Original post by 4Ed)
the first integrates perfectly to 1/3 e^x^3. differentiate it and see for yourself.
the second one is basically integrate between 1 and 3, pi y^2 dx.
so it's the integral of pi e^3x = 1/3 pi e^3x, between limits 1 and 3. so your answer should be 1/3 pi (e^9  e^3).
i hope that's right 
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 01062004 13:27
(Original post by SUKBarracuda)
I think bezza and mockel have accidently put e^3 in the brackets, but e^9 = e^3 x e^6, and not e^3 x e^3! 
Hoofbeat
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 01062004 18:37
(Original post by SUKBarracuda)
I can indeed.
The volume of a rotated shape is the (pi) x ∫y² dx
This gives (pi) x ∫(e^(3x/2))^2 dx (Between limits 1 and 3)
= (pi) x ∫e^(3x) dx
= (pi)[(1/3)(e^3x)] between 1 and 3
Take out the factors 1/3 and e^3 gives::
(1/3)(pi)e³[ e^6  1]
I think bezza and mockel have accidently put e^3 in the brackets, but e^9 = e^3 x e^6, and not e^3 x e^3!
Hope this helps 
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 01062004 18:48
(Original post by Hoofbeat)
Thanks for all your help. However, i am slightly confused. surely 3^[3x/2] all squared would give e^[9x^2/4]? Oh god, how am I going to get my A in P3 if i can't even do simple indices!!! 
SUKBarracuda
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 01062004 19:01
Bezza is right. e^(3x/2) all squared is the same as:
e^(3x/2) x e^(3x/2)
which is e^((3x/2) x 2)
which is e^(3x).
You can think of the indice theory in terms of 2s.
2^4 = 16
so (2^4) all squared is 16 x 16 which equals 256.
and this is equal to 2^8, which is of course the same as 2^(4x2).
But don't worry you'll do fine in the exam if you just practice a bit of algebra over the next week. 
Hoofbeat
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 01062004 19:22
(Original post by SUKBarracuda)
Bezza is right. e^(3x/2) all squared is the same as:
e^(3x/2) x e^(3x/2)
which is e^((3x/2) x 2)
which is e^(3x).
You can think of the indice theory in terms of 2s.
2^4 = 16
so (2^4) all squared is 16 x 16 which equals 256.
and this is equal to 2^8, which is of course the same as 2^(4x2).
But don't worry you'll do fine in the exam if you just practice a bit of algebra over the next week. 
Silly Sally
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 01062004 19:28
This is related to integration (i promise!!! !!!)
Ok in the above question, you have to integrate e^(3x), so i was wondering what is the integral of something like e^(3(x^2))
Thanks 
IntegralAnomaly
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 01062004 21:03
(Original post by Silly Sally)
This is related to integration (i promise!!! !!!)
Ok in the above question, you have to integrate e^(3x), so i was wondering what is the integral of something like e^(3(x^2))
Thanks 
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 01062004 22:20
(Original post by IntegralAnomaly)
u cannot express the integral of e^x^2 in terms of elementary functions,but u can find the exact value of the area under the graph of y=e^x^2.
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