If `f(alpha)=f(beta)` and `n in N`, then the value of `int_alpha^beta (g(f(x)))^n g\'(f(x))*f\'(x)dx=` (A) `1` (B) `0` (C) `(beta^(n+1)-alpha^(n+1))/(n+1)` (D) none of these

If (x+1)+f(x-1)=2f(x)andf(0),=0 then f(n),n in N, is nf(1)(b){f(1)}^(n)(c)0 (d) none of these

For every integer n, int_(n)^(n+1)f(x)dx=n^(2) , then the value of int_(0)^(5)f(x)dx=

If a+alpha=1,b+beta=2 and af(n)+alphaf(1/n)=bn+beta/n , then find the value of (f(n)+f(1/n))/(n+1/n)

Let int_(alpha)^( beta)(f(alpha+beta-x))/(f(x)+f(alpha+beta-x))dx=4 then

If alpha,beta(beta>alpha), are the roots of g(x)=a x^2+b x+c=0 and f(x) is an even function, then int_alpha^betae^(f((g(x))/(x-alpha)))/(e^(f((g(x))/(x-alpha)))+e^(f((g(x))/(x-beta))))= (a)|b/(2a)| (b) (sqrt(b^2-4a c))/(|2a|) (c)|b/a| (d) none of these

If f(x)=alpha x+beta and f(0)=f^(1)(0)=1 then f(2) =

If f(x)=alpha x^(n), prove that alpha=(f'(1))/(n)