To the contrary, I think that the original example is appropriate
for the intended audience (first year undergraduates).
Most of these students haven't heard of the Beta integral.

Yours truly, Lady Sue

http://www.highway.org

Why not consider the more general problem of 

f(x) = x^{p} (1-x)^{q}

since I find the above example is too specific and the general
problem is more interesting because f(x) is the integrand of
the Beta integral. 

Just a suggestion, Sir Isaac