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 utt = c2uxx.
Do not use the Leibnitz Rule, but instead review the
Fundamental Theorem of Calculus.
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.