please delete

[lisasayzhi]

please delete

 

[pka]

There is no elementary closed form for \(\displaystyle \L
\int {xe^{x^4 } dx}\).

However, \(\displaystyle \L
xe^{x^4 } = \sum\limits_{n = 0}^\infty {\frac{{x^{4n + 1} }}{{n!}}}\) which can be integrated term by term.
So one can get a good approximation.

 

[Unco]

Re: Definite Integrals

Could someone please tell me if I am doing this problem correctly?

1)Evaluate $\displaystyle \int xe^{x^2} dx$ from 0 to 2
$\displaystyle u=x^2 \frac{1}{2}du=xdx$
$\displaystyle \frac{1}{2} \int e^u du$
$\displaystyle =\frac{e^u}{2}$
$\displaystyle =\frac{e^{x^2}}{2}$
$\displaystyle \frac{e^{2^2}}{2} - \frac{e^{0^2}}{2}$
$\displaystyle =\frac{e^4}{2} - \frac{1}{2}$

Nice work, Lisa.