Finding an Integral from an Unknown Function

[Khayyam89]

Homework Statement

If xsin$$\pi$$x = $$\int$$f(t) dt, where is a continuous function, find f(4).
b=x², a=0

Homework Equations

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?

 

[HallsofIvy]

Yes, if
[tex]x sin(\pi x)= \int_0^{x^2} f(t)dt[/quote]<br /> 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:<br /> $$F(x)= \int_0^x^2 f(t)dt= \int_0^u f(t)dt$$<br /> 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 $x sin(\pi x)$?<br /> $$f($$[/tex]