#### assume, multiple assumptions (16.3.98)

The function p(k,n) with k,n Integer and n>=k>=0 is deﬁned as follows.

I want maple to solve int(x^k*(1-x)^(n-k)*binomial(n,k), x=0..1); . It is = 1/(n+1); (with
integration by parts)

Deﬁnite integration: Can’t determine if the integral is convergent. Need to know the sign of
--> -n+k

Will now try indeﬁnite integration and then take limits. Has someone written a program to solve this
problem?

To obtain the expected result of this calculation it is necessary to use a little caution in the way
assumptions are declared. In particular, the assume command overrides previous assumptions; to add
assumptions the additionally command should be used. To illustrate the diﬀerence, use the about
command to query the current assumptions about a speciﬁc Maple name. All of this, together with the
simpliﬁcations necessary to obtain the simpliﬁed form for your integral are contained in the Maple
session attached to the end of this message.