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

If f(x) = {{:(0,",""where" x = (n)/(n+1) n = 1"," 2"," 3"......"),(1,"," "else where"):},, then the value of int_(0)^(2) f(x)dx.

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

suppose for every integer n, int_n^(n+1)f(x)dx=n^2 then the value of int_(-2)^4 f(x)dx is

If for every ineger n , int_(n)^(n+1) f(x) dx=n^(2) then the value of int_(-2)^(4) f(x)dx=

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