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Integration

Fun integration problem:

Integrate e^(x^2)
and it isn't (e^(x^2))/2x

any answers?
Reply 1
Avatar for Aylia
Aylia
1
I think.. but I'm not sure, that its 2xe^(x^2)
Reply 2
Avatar for Nylex
Nylex
10
Aylia
I think.. but I'm not sure, that its 2xe^(x^2)


If you differentiate that, you get 2e^x^2 + 4x^2.e^(x^2)

You can't integrate e^(x^2) by methods you've probably learnt (ie. parts and substitution), I'm not even sure how you would do that.
Reply 3
Avatar for Aylia
Aylia
1
sorry that was stupid didn't read the question properly lol
Reply 4
Avatar for Aylia
Aylia
1
http://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/intbypartssoldirectory/IntByPartsSol3.html#SOLUTION%2016

Can't work out if that helps or not...
Reply 5
Avatar for Aylia
Aylia
1
How about Ln?

y = e^(x^2)
ln y = x^2 ln e
ln y = x^2 ( ln e is 1 yes?)
Reply 6
Avatar for Bhaal85
Bhaal85
9
Aylia
How about Ln?

y = e^(x^2)
ln y = x^2 ln e
ln y = x^2 ( ln e is 1 yes?)


You can't presume Y=f(X).
Reply 7
Avatar for fishpaste
fishpaste
Hm yes, I know you can integrate xe^x^2 using function and derivative, but straight e^x^2, I'll have a think.
Reply 8
Avatar for Nylex
Nylex
10
Aylia
How about Ln?

y = e^(x^2)
ln y = x^2 ln e
ln y = x^2 ( ln e is 1 yes?)


That's right, but you could have just missed out that middle line :smile:.
Reply 9
Avatar for Aylia
Aylia
1
Nylex
That's right, but you could have just missed out that middle line :smile:.



yay! :smile: have spent ages thinking about that!
http://www.nrich.maths.org/discus/messages/27/7774.html?1078054281
Reply 11
Avatar for animal555
animal555
are u doing AS Level, P2?, in which case are u sure it wasn't e^(2x). If so the answer would be (1/2)e^(2x).
You can't integrate this directly, I'm pretty sure its called the gamma function. Between -infinity and infinity its value is root(2pi).
Sir I. Newton
You can't integrate this directly, I'm pretty sure its called the gamma function. Between -infinity and infinity its value is root(2pi).

Its not the gamma function,thats gotta do with x!.
To integrate e^x^2 u have to use a mixture of double integrals and converting from normal integration to polar integration etc etc.
Its degree level stuff(thats how u integrate the normal distribution function)
yipee. i remember doing htis a few weeks ago, and i've already forgotten ( :rolleyes: ). something to do with integrating r^x e^r² between 0 and infinity.

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