`int_(0)^(1)x^(2)(1-x)^(n)dx`

U_(n)=int_(0)^(1)x^(n)(2-x)^(n)dx and V_(n)=int_(0)^(1)x^(n)(1-x)^(n)dx,n in N and if (V_(n))/(U_(n))=1024, then the value of n is

Find the value of int_(0)^(1)x(1-x)^(n)dx

The value of (^nC_(0))/(n)+(^nC_(1))/(n+1)+(^nC_(2))/(n+2)+....+(n)/(2n) is equal to a.int_(0)^(1)x^(n-1)(1-x)^(n)dxbint_(1)^(2)x^(n)(x-1)^(n-1)dxc*int_(1)^(2)x^(n-1)(1+x)^(n)dx d.int_(0)^(1)(1-x)^(n-1)dx

If m, n in N , then l_(m n) = int_(0)^(1) x^(m) (1-x)^(n) dx is equal to

If I(m,n)=int_(0)^(1)x^(m-1)(1-x)^(n-1)dx,(m,n in I,m,n>=0),th epsilonI(m,n)=int_(0)^(oo)(x^(m-1))/((1+x)^(m-n))dxI(m,n)=int_(0)^(oo)(x^(m-1))/((1+x)^(m+n))dxI(m,n)=int_(0)^(oo)(x^(n-1))/((1+x)^(m+n))dxI(m,n)=int_(0)^(oo)(x^(n))/((1+x)^(m+n))dx

If I(m,n)=int_(0)^(1)x^(m-1)(1-x)^(n-1)dx, then

int_(0)^(1)(1-x^(3))^(n)dx=

" 2."int_(0)^(1)(x^2)/(1+x^(3))dx