If `U_n=int_0^1x^n(2-x)^ndxa n dV_n=int_0^1x^n(1-x)^n dx ,n in N ,` and if `(V_n)/(U_n)=1024 ,` then the value of `n` is________

For U_(n)=int_(0)^(1)x^(n)(2-x)^(n)dx;V_(n)=int_(0)^(1)x^(n)(1-x)^(n)dxn in N which of the following statement(s) is/are true? (a) U_(n)=2^(n)V_(n)( b) U_(n)=2^(-n)V_(n)(c)U_(n)=2^(2n)V_(n)(d)V_(n)=2^(-2n)U_(n)

If I_(n)=int_(0)^(1)x^(n)e^(-x)dx for n in N, then I_(7)-I_(6)=

If = int_(0)^(1) x^(n)e^(-x)dx "for" n in N "then" I_(n)-nI_(n-1)=

int_(n)^(n+1)f(x)dx=n^(2)+n then int_(-1)^(1)f(x)dx=

If I_(n)=int(x^(n))/(1+x^(2))dx, where n in N , then : I_(n+2)+I_(n)=

If u _(n) = int _(0) ^(pi//2) x ^(n) sin x dx, n in N then the value of u _(10) + 90 u _(s) is