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

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

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

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

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

Let I_(n)=int_(0)^(pi//2) sin^(n)x dx, nin N . 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_(1)=int_(0)^(oo) (dx)/(1+x^(4))dx and I_(2)underset(0)overset(oo)int dx"then"n (I_(1))/(I_(2))=

If I_(n)=int(x^(n)dx)/(sqrt(x^(2)+a)) then prove that I_(n)+(n-1)/(n)al_(n-2)=(1)/(n)x^(n-1)*sqrt(x^(2)+a)

If I_(n)=int_(0)^(1)(1-x^(5))^(n)dx, then (55)/(7)quad (I_(10))/(I_(11)) is equal to

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