- #1

richyw

- 180

- 0

## Homework Statement

I have the function[tex]u(x,t)=\frac{1}{2c}\int^{x+ct}_{x-ct}g(\xi)d\xi[/tex]where g is continuously differentiable and c is a constant. I need to verify that this is a solution to the wave equation.

## Homework Equations

My prof gave me the formula[tex]\frac{d}{dt}\int^{b(t)}_{a(t)}F(y,t)dy=\int^{b(t)}_{a(t)}F_t(y,t)dy+F(b(t),t)b'(t)-F(a(t),t)a'(t)[/tex]

## The Attempt at a Solution

I really don't see how I can use this rule when trying to take these derivatives. The [itex]\xi[/itex] is really messing me up. Do I need to use this rule right off the bat on my first derivative (I am trying to take the x derivatives first). It seems like this question is just as easy as using a formula, but I cannot seem to get an answer that works out...