ok integral of INT/limits 1 to 0/ (e^x)^2

Question

anonymous · Answer

rewrite?

anonymous · Answer

$$\int_0^1 e^{x^2}dx$$

anonymous · Answer

ah it is error function or something like that I can't do it

anonymous · Answer

http://www.wolframalpha.com/input/?i=integration+e^%28x^2%29+from+0+to+1

agreene · Answer

yeah, i think its like 
1/2 sqrt(pi)*error(imaginary) or some such

anonymous · Answer

yep. that's what my calcu says.. 1.462651746 xD

anonymous · Answer

what is this now ?

anonymous · Answer

nonono, (e^x)(e^x) or (e^x)^2, integrate that from 1 to 0

anonymous · Answer

And I have a computer right in front of me as well as a ti-84+ so I dont want your calculator or wolfram alpha answers please :)

agreene · Answer

Oh, that is much simpler.
(e^x)^2 = e^2x 
so:
$$\int\limits_{0}^{1}e^{2x}dx=\frac{1}{2}e^2x$$
take it to the limits:
[1/2*e^(2)]-[1/2*e^(0)]=1/2e^2-1/2
factor it and you have:
$$\frac{1}{2}(e^2-1)$$

anonymous · Answer

oh you sure that (e^x)^2=e^2x?

agreene · Answer

yes, that is one of the properties of exponents

anonymous · Answer

fsho