Thread: monotone increasing

Let f : [a, b] -> R be a positive continuous function, i.e., f(x) >= 0 for all x in [a, b].

I want to show that the function F : [a, b] -> R defined as F(x) = integral of f with limits x and a, for x in [a, b] is monotone increasing (i.e., F(x) >= F(y) if x >= y).

any ideas? thankz

Originally Posted by dopi

Let f : [a, b] -> R be a positive continuous function, i.e., f(x) >= 0 for all x in [a, b].

I want to show that the function F : [a, b] -> R defined as F(x) = integral of f with limits x and a, for x in [a, b] is monotone increasing (i.e., F(x) >= F(y) if x >= y).

any ideas? thankz

Okay, you have the function

It exists since all continous functions are integrable.
Now, what ails me is that the upper limit is , I think you wanted to write thus hence the function,

The derivative of this function is (2nd fun. the. of cal.)

Thus the function is decreasing NOT increasing.

Thus, I think you wanted to write,

Then using the above concepts it is increasing on

Originally Posted by ThePerfectHacker

Okay, you have the function

It exists since all continous functions are integrable.
Now, what ails me is that the upper limit is , I think you wanted to write thus hence the function,

The derivative of this function is (2nd fun. the. of cal.)

Thus the function is decreasing NOT increasing.

Thus, I think you wanted to write,

Then using the above concepts it is increasing on

With this question that i posted i denoted F(x) = integral of f with upper limit x and lower limt alpha, but you have added (t) as in f(t), where as iv just wrote f, so i think it might be an riemann integra....does this affect the ansower of the question to what you have done?
thankz