If m and n are positive integers and `f(x) = int_1^x(t-a )^(2n) (t-b)^(2m+1) dt , a!=b`, then

If f(x) = int_1^x (1)/(2 + t^4) dt ,then

If (x-a)^(2m) (x-b)^(2n+1) , where m and n are positive integers and a > b , is the derivative of a function f then-

If (x-a)^(2m) (x-b)^(2n+1) , where m and n are positive integers and a > b , is the derivative of a function f then-

If (x-a)^(2m)(x-b)^(2n+1), where m and n are positive integers and a>b, is the derivative of a function f then-

A periodic function with period 1 is integrable over any finite interval.Also,for two real numbers a,b and two unequal non-zero positive integers m and nint_(a)^(a+n)f(x)dx=int_(b)^(b+m)f(x) calculate the value of int_(m)^(n)f(x)dx

If x,y are positive real numbers and m, n are positive integers, then prove that (x^(n) y^(m))/((1 + x^(2n))(1 + y^(2m))) le (1)/(4)

If x,y are positive real numbers and m, n are positive integers, then prove that (x^(n) y^(m))/((1 + x^(2n))(1 + y^(2m))) le (1)/(4)