- #1

- 11

- 0

## Homework Statement

Verify that, for any continuously differentiable function g and any constant c, the function

￼u(x, t) = 1/(2c)∫

^{(x + ct)}

_{(x - ct)}g(z) dz ( the upper limit (x + ct) and lower limit (x - ct))

is a solution to the PDE u

_{tt}= c

^{2}u

_{xx}.

Do not use the Leibnitz Rule, but instead review the

Fundamental Theorem of Calculus.

## Homework Equations

Fundamental Theorem of Calculus I & II.

## The Attempt at a Solution

Not a clue but tried the first and second fundamental theorem of calculus (learned in calc I or II) but did not seem to get anywhere.