# 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
$$x\int_1^xf(u)du$$