Need Help with Integral : undefined function integrand

[barnator]

$\int_0^{y-x} (y-x)^3f[x] dx$

I really don't know what integration method that should be used to solve this. I would really appreciate anyone pointing me in the right direction, this problem is frustrating me! I tried integration by parts but it doesn't really get me anywhere.

 

[LCKurtz]

$\int_0^{y-x} (y-x)^3f[x] dx$

I really don't know what integration method that should be used to solve this. I would really appreciate anyone pointing me in the right direction, this problem is frustrating me! I tried integration by parts but it doesn't really get me anywhere.

What does f[x] mean? No hope of working the problem without knowing.

 

[HallsofIvy]

The whole problem makes no sense. In addition to f being undefined, you should not have the "integration variable", x, in the upper limit of integration- it makes no sense to say that x varies from 0 to x- y.

 

[barnator]

OK thanks for the help. I guess the problem I have has some typos.

I have a related question though referring to the Integral theorem under http://www.atp.ruhr-uni-bochum.de/rt1/syscontrol/node145.html

I'm confused about the work at the integration by parts. It looks like he sets $u = \int_0^t f[\tau] d\tau$ and $dv = e^{-st} dt$, so that he ends up with $du = f[t]dt$. I'm not following how to go from u to du.

 

[Muphrid]

Let the antiderivative of $f$ be $F$.

By the fundamental theorem of calculus,

$$\int_0^t f(\tau) \; d\tau = F(t) - F(0)$$

Clearly, the derivative of this result is $F'(t) = f(t)$.