Evaluate \( \int_{0}^{1}(t x+1-x)^{n} d x \)
where \( n \) is a positive integer and \( t \) is ...
Evaluate \( \int_{0}^{1}(t x+1-x)^{n} d x \)
where \( n \) is a positive integer and \( t \) is a parameter
P independent of \( x \). Hence, show that
VW \( \int_{0}^{1} x^{k}(1-x)^{n-k} d x=\frac{1}{{ }^{n} C_{k}(n+1)} \), for \( k=0,1, \ldots, n \).
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