Let `f(a) gt 0`, and let f(x) be a non-decreasing continous function in [a,b]. Then, `(1)/(b-a)int_(a)^(b) f(x) dx` has the

Let f(a)>0, and let f(x) be a non- decreasing continuous function in [a,b]. Then,(1)/(b-a)int_(a)^(b)f(x)dx has the

Let f(a)>0 , and let f(x) be a non-decreasing continuous function in [a, b] . Then, 1/(b-a)int_a^bf (x) dx has the

Property 4: If f(x) is a comtinuous function on [a;b] then int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx

Let f(x), xge0 , be a non-negative continous function,and let F(x) = int_(0)^(x)f(t)dt, xge0 , if for some cgt0,f(x)lec F(x) for all xge0 , then show that f(x)=0 for all xge0 .

Let a gt 0 and f(x) is monotonic increase such that f(0)=0 and f(a)=b, "then " int_(0)^(a) f(x) dx +int_(0)^(b) f^(-1) (x) dx is equal to