Let `I_(n)=int_(0)^(1)x^(n)sqrt(1-x^(2))dx.` Then `lim_(nrarroo)(I_(n))/(I_(n-2))=`

Let I_(n) = int_(0)^(1)x^(n)(tan^(1)x)dx, n in N , then

Let I_(n) = int_(0)^(1)(1-x^(3))^(n)dx, (nin N) then

Let I_(n) = int_(0)^(1)(1-x^(3))^(n)dx, (nin N) then

Let I_(n)=int_(0)^(pi//2) sin^(n)x dx, nin N . Then

Let I_(n)=int_(0)^(pi//2) sin^(n)x dx, nin N . Then

Let I_(n) = int_(0)^(1//2)(1)/(sqrt(1-x^(n))) dx where n gt 2 , then

If I_(n)=int_(0)^(1)x^(n)(tan^(-1)x)dx, then prove that(n+1)I_(n)+(n-1)I_(n-2)=-(1)/(n)+(pi)/(2)

If I_(n)=int_(0)^(pi//4) tan^(n) x dx then {:(" " Lt),(n rarr oo):}n(I_(n)+I_(n+2))=

Let f(x) = {{:((x)/(sin x) ",",x in "(0,1)"),(1",",x=0):} Consider the integral I_(n) = sqrt(n)int_(0)^(1//n) f(x)e^(-n x)dx . Then lim_(n rarr infty) I_(n)

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