Chapter 13.9, Problem 6P

Continue the problem of Example 2 in the following way: Instead of using the explicit form of $B(k)$ from $(9.12),$ leave it as an integral and write (9.13) in the form $u(x,y)=\frac{200}{\pi }{\displaystyle {\int }_0^{\infty }{e}^{-ky}}\sin kxdk{\displaystyle {\int }_0^1\sin }ktdt$.

Change the order of integration and evaluate the integral with respect to $k$ first. (Hint: Write the product of sines as a difference of cosines.) Now do the $t$ integration and get (9.14).