# Homework Help: Finding an Integral from an Unknown Function

1. Dec 2, 2008

### Khayyam89

1. The problem statement, all variables and given/known data
If xsin$$\pi$$x = $$\int$$f(t) dt, where is a continous function, find f(4).
b=x2, a=0

2. Relevant equations

3. The attempt at a solution
I assumed that the problem dealt with the Fundamental Theroem of Calculus so I began by saying that g(x)=xsin$$\pi$$x but that is as far as it makes sense to me. Could anyone confirm to me that I am following the correct path?

2. Dec 2, 2008

### HallsofIvy

Yes, if
$$x sin(\pi x)= \int_0^{x^2} f(t)dt[/quote] you can apply the Fundamental theorem but if you do that, because the upper limit is "x2" rather than "x", you need to use the chain rule also: [tex]F(x)= \int_0^x^2 f(t)dt= \int_0^u f(t)dt$$
where u= x2. The derivative of the right hand side is F'(u)(du/dx)= f(u)(2x)= f(x2)(2x). That is equal to the derivative of the left hand side. What is the derivative of $x sin(\pi x)$?
[tex]f(