If `f(x)={0` ,where `x=n/(n+1),n=1,2,3.... and 1` else where then the value of `int_0^2 f(x) dx` is

The value of int _(0)^(2)f(x) d x , where f(x)={(0",where" x = (n)/(n+1)", n=1,2,3" ...) ,(1"," "elsewhere"):}3 is equal to

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

For each ositive integer n, define a function f _(n) on [0,1] as follows: f _(n((x)={{:(0, if , x =0),(sin ""(pi)/(2n), if , 0 lt x le 1/n),( sin ""(2pi)/(2n) , if , 1/n lt x le 2/n), (sin ""(3pi)/(2pi), if, 2/n lt x le 3/n), (sin "'(npi)/(2pi) , if, (n-1)/(n) lt x le 1):} Then the value of lim _(x to oo)int _(0)^(1) f_(n) (x) dx is:

If f(x)=(2011 + x)^(n) , where x is a real variable and n is a positive interger, then value of f(0)+f'(0)+ (f'' (0))/(2!)+...+ (f^((n-1))(0))/((n-1)!) is -f(0)+f'(0)+ (f'' (0))/(2!)+...+ (f^((n-1))(0))/((n-1)!) is -

Define a function f:R rarr R by f(x)=max{|x|,|x-1|,...|x-2n|} where n is a fixed natural number then int_(0)^(2n)f(x)dx is

Suppose for every integer n, .int_(n)^(n+1) f(x)dx = n^(2) . The value of int_(-2)^(4) f(x)dx is :

If f(x) is a polynomial of degree n such that f(0)=0,f(x)=(1)/(2),...,f(n)=(n)/(n+1) then the value of f(n+1) is

If A=int_0^1 x^50(2-x)^50dx, B=int_0^1 x^50(1-x)^50dx and A/B=2^n , then the value of n is …

Let f(x)-|x-1|+|x-2| . I = int_(0)^(1)f(x)dx , M - the minimum value of f , N=f'(x) for x < - 4 and C- the value of f''(4) .Then the value of (M^(2)-N^(2)-IC)/(2) is :