What does this notation mean in terms of differentiation?

[Firepanda]

http://img442.imageshack.us/img442/6018/scoreqt9.jpg

Can someone explain what this notation means regarding differentiating please.

I've never seen it this way using the integration symbol, so I have no idea where to start.

:) thx

 

[quasar987]

Well for instance the first question asks you to find the derivative wrt x of the function F(x) defined by

F(x)=\int_{1}^x\ln(t)dt

hint: think fundamental theorem of calculus

 

[Firepanda]

F(x)=\int_{1}^x\f(t)dt then dF/dx=f(x)

*hopes his latex command worked*

So I am supposed to differentiate F(x), which will then give me f(x) as my answer?

 

[Firepanda]

lol that went tits up, ill try again

F(x)=\int_{1}^x\f(t)dt\then dF/dx=f(x)

 

[Firepanda]

1 more try :( :

F(x)=\int_{1}^x\f\(t)dt\<br /> <br /> then dF/dx=f(x)

 

[Firepanda]

K nevermind :D

but do I just calculate the integral as F(x), then differentiate F(x) with respect to x, which is then my answer?

 

[quasar987]

There is an "edit" button right next to "quote" and "multiquote" in the bottom right of each post that let's you edit the latex in case you mess up.

The answer to your last question is yes.

But you're going to run into difficulties when you try to do (ii) with this method because there are no primitives of e^{-t²} in terms of elementary functions... so you will have to use a slightly more sophisticated approach.

 

[quasar987]

the whole point of what?

write what in integral form?

"represented"?