Finding an Integral from an Unknown Function

[Khayyam89]

Homework Statement

If xsin\pix = \intf(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\pix 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
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 &quot;x²&quot; rather than &quot;x&quot;, 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&#039;(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(