Having a hard time understanding how the function is actually defined.

[SimenReynolsd]

Hello, first time here

I have something here that I'm not really sure how to begin with. It goes like this:
The function F : |R → |R is defined by:

F (x) = the integral from 0 to x of f(t) dt.

(How do you add integration signs?)

I have a range of questions to answer around this core function, but I have a really har time figuring out where to start.
In one of the questions for example, I need to show that F'(x) is greater than 0 for all values of x, so as to prove that the function is strictly growing. But as far as I can tell, the derived of the function here would be the integral from 0 to x of f(t) dt... But that's not really much to work with.

Anyone able to help? Am I just horribly confused?

 

[fatemeh8989]

Hello, first time here

I have something here that I'm not really sure how to begin with. It goes like this:
The function F : |R → |R is defined by:

F (x) = the integral from 0 to x of f(t) dt.

(How do you add integration signs?)

I have a range of questions to answer around this core function, but I have a really har time figuring out where to start.
In one of the questions for example, I need to show that F'(x) is greater than 0 for all values of x, so as to prove that the function is strictly growing. But as far as I can tell, the derived of the function here would be the integral from 0 to x of f(t) dt... But that's not really much to work with.

Anyone able to help? Am I just horribly confused?

I am not sure I understand your question well, but the formula can help you:
dIntegral f(t)/dx (integral from 0 to x ) = f(x)

and if the integral be from 0 to U(x) it becomes U'(x)*f(x)
am I clear?

 

[srmichael]

Hello, first time here

I have something here that I'm not really sure how to begin with. It goes like this:
The function F : |R → |R is defined by:

F (x) = the integral from 0 to x of f(t) dt.

(How do you add integration signs?)

I have a range of questions to answer around this core function, but I have a really har time figuring out where to start.
In one of the questions for example, I need to show that F'(x) is greater than 0 for all values of x, so as to prove that the function is strictly growing. But as far as I can tell, the derived of the function here would be the integral from 0 to x of f(t) dt... But that's not really much to work with.

Anyone able to help? Am I just horribly confused?

So what you have is \(\displaystyle F(x)=\int_0^xf(t)dt\)

What else did the problem give you to work with?

 

[SimenReynolsd]

Gah, I feel terribly stupid now, as it turned out, there was an earlier assignment on the previous page wherein f(x) was defined, and by extent also f(t) So now it's just a regular piece of math.

I hope too many of you didn't cook your noggins on this one...

For anyone curious the initial function was f(x) = (arctanx)/x for all values of x except 0, and f(x) = 1 for x = 0.

Again, sorry to waste your time...

EDIT: Wow... I just realized how much flu + lack of sleep had gotten to me... When I signed up I actually managed to misspell my own name...