Definite integration

數學小子

1)  in(0 to 1)x^^m(1-x)ⁿdx
2)  lim(x->inf.)[in(0 to x)e^{t^2}dt]²/[in(0 to x²)e^tdt]

-終場ソ使者-

1)
Let


,
It's not hard to imagine that
,




2)
This is an case, therefore L'Hospital rule is used



it's still , L'Hospital rule is used again