If `I(m,n)=int_0^1 t^m(1+t)^n.dt`, then the expression for I(m,n) in terms of I(m+1,n-1) is:

IfI(m , n)=int_0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m-n))dx I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m+n))dx I(m , n)=int_0^oo(x^(n-1))/((1+x)^(m+n))dx I(m , n)=int_0^oo(x^n)/((1+x)^(m+n))dx

If int_0^1(e^t)/(1+t)dt=a , then find the value of int_0^1(e^t)/((1+t)^2)dt in terms of a .

If I_n=int( lnx)^n dx then I_n+nI_(n-1)

IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx , Then show that I_(m , n)=(m-1)/(m+n)I_m-2n(m ,n in N) Hence, prove that I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4 when both m and n are even ((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))

Let m,n be two positive real numbers and define f(n)=int_(0)^(oo)x^(n-1)e^(-x)dx and g(m,n)=int_(0)^(1)x^(m-1)(1-m)^(n-1)dx . It is known that f(n) for n gt 0 is finite and g(m, n) = g(n, m) for m, n gt 0. int_(0)^(oo)(x^(m-1))/((1+x)^(m+n))dx=

Let I_(n)=int_(0)^(pi//2)(sinx+cosx)^(n)dx(nge2) . Then the value of n. I_(n)-2(n-1)I_(n-1) is

The integral value of m for which the root of the equation m x^2+(2m-1)x+(m-2)=0 are rational are given by the expression [where n is integer] (A) n^2 (B) n(n+2) (C) n(n+1) (D) none of these

If sum of m terms is n and sum of n terms is m, then show that the sum of (m + n) terms is -(m + n).

If t_(n)" is the " n^(th) term of an A.P. then the value of t_(n+1) -t_(n-1) is ……