Solution
= Solution
The substitution $t\mapsto1-t$ gives $B(p,q)=B(q,p)$. Direct integration gives
$$
\boxed{B(1,q)=\int_0^1(1-t)^{q-1}dt=\frac1q}.
$$
= Solution
The substitution $t\mapsto1-t$ gives $B(p,q)=B(q,p)$. Direct integration gives
$$
\boxed{B(1,q)=\int_0^1(1-t)^{q-1}dt=\frac1q}.
$$