Question

integral of e power x^2 =?

Answer 1

\[\int\limits e^{x^{2}}dx ?\]

Answer 2

Is that the problem?

Answer 3

yep

Answer 4

Do you know what a power series expansion is ?

Answer 5

Since there is no elementary anti-derivative you have to expand it as a power series
\[e^x=\sum_{n=0}^\infty {x^n \over n!}\]
\[e^{x^2}=\sum_{n=0}^\infty {x^{2n} \over n!}\]
\[\int\limits_{a}^{b} e^{x^2}dx=\sum_{n=1}^\infty \int\limits_{a}^{b} {x^{2n} \over n!}dx\]
\[\int\limits\limits_{a}^{b} e^{x^2}dx=\sum_{n=1}^\infty {x^{2n+1} \over{ (2n+1)n!}}|_a^b\]
\[\int\limits\limits\limits_{a}^{b} e^{x^2}dx=\sum_{n=1}^{\infty} {b^{2n+1} \over (2b+1)n!}-\sum_{n=1}^{\infty} {a^{2n+1} \over (2a+1)n!}\]

Answer 6

but it is so complicated!!!!!!

Answer 7

That integral is famous for being difficult, (also n should go from 1 in the first 2 lines)

Answer 8

seriously, it is. how do i understand power series method of solving differential equations

Answer 9

integral is soooooooooooooooooooo damemmmmmmmm easy
but only the series puts me in trouble thats it!!!!!!1

Answer 10

for emanumak:
http://www.stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/upfiles/3c3-UseSeries-SolveDEs_Stu.pdf

Actually the series part makes the integral very easy since it turns it into an infinite sum of polynomials

Answer 11

thanks a dozen, konfab