Riemann-Stieltjes integral with f(x)=x and α(x)=x²

[prudens2010]

Let f = 

x, for 0<=x<=1
1, for 1<x

alpha =

x^2, for 0<=x<=1
1, for 1<x

Find Integral (f) d(alpha) -- from 0 to 23

pls help!

 

[Newtime]

Let f = 

x, for 0<=x<=1
1, for 1<x

alpha =

x^2, for 0<=x<=1
1, for 1<x

Find Integral (f) d(alpha) -- from 0 to 23

pls help!

Use the definition of the R-S integral. The answer should pop right out unless I'm missing something. Where does the problem lose you?

 

[mathman]

This case easily translates into an ordinary Riemann integral.
dα = 2xdx, 0≤x≤1
dα = 0, x>1