When is it important to try to determine the credibility of a source? Why is it important?

Because the audience will expect you to back up your assertions with credible evidence. If you don't get it from a credible source the audience will not be convinced that the claim is correct or plausible.

Credible sources, therefore, must be reliable sources that provide information that one can believe to be true. It is important to use credible sources in an academic research paper because your audience will expect you to have backed up your assertions with credible evidence.