Can anyone check my work here and if I went wrong, tell where and how and why etc etc. Thanks!

Question:

Decide whether the improper integral converges or diverges and if it converges, give it's value:

discontinuous at x=9, so rewrite the right endpoint in terms of a limit:

substitute u=9-x, and since this is a definite integral, we need to change the limits of integration:

Thus the limit equals a finite number, and the integral converges to .