>>438
ｋの値を変えてプログラムで実験してみたけど
> # ∫sin(x^k)dx[0∫sin(x^k)dx[0→∞]

> f <- function(k) integrate(function(x)sin(x^k),0,Inf)
> f(1)
Error in integrate(function(x) sin(x^k), 0, Inf) :
roundoff error is detected in the extrapolation table
> f(runif(1,1,10))
Error in integrate(function(x) sin(x^k), 0, Inf) :
maximum number of subdivisions reached
> f(runif(1,0,1))
Error in integrate(function(x) sin(x^k), 0, Inf) :
roundoff error is detected in the extrapolation table
> f(runif(1,-1,0))
Error in integrate(function(x) sin(x^k), 0, Inf) :
the integral is probably divergent
> f(runif(1,-10,-1))
Error in integrate(function(x) sin(x^k), 0, Inf) :
the integral is probably divergent

収束はしないみたい。