How do you find the derivative of this integral?

1. Jan 16, 2005

KataKoniK

$$\int_{0}^{x} [t \int_{1}^{t} f(u)du] dt$$

I don't know what to do. Thanks in advance

Last edited: Jan 16, 2005
2. Jan 16, 2005

dextercioby

1.1-st is to write the formula properly.

Did u mean

$$\frac{d}{dx}\{\int_{0}^{x} t[\int_{1}^{t} f(u)du] dt\}$$

??

Daniel.

3. Jan 16, 2005

KataKoniK

Yeah, that's it, but with no d/dx in the beginning. Sorry, I'm new to this latex stuff.

$$\int_{0}^{x} [t \int_{1}^{t} f(u)du] dt$$

4. Jan 16, 2005

dextercioby

Okay,how about applying some Fundamental Theorem of calculus??

Daniel.

5. Jan 17, 2005

HallsofIvy

Staff Emeritus
Your TITLE is "How do you find the derivative of this integral". That was why dextercioby put in the "d/dx".

Fundamental theorem of calculus! $$\frac{d}{dx}\int_a^xF(t)dt= F(x)$$.

Here, F(t) is $$t \int_{1}^{t} f(u)du] dt$$ so the derivative is
$$x\int_1^xf(u)du$$