The evaluation of quantum integrals

Rather a long time after its publication, my attention was drawn to a paper by Mr. E. C. Kemble(1) dealing with the evaluation of the integral J = 2 b∫a √f(q) dq, where a and b denote the roots of the radicand. Before preparing his own method of computation, Mr. Kemble criticizes two procedures used by other authors and rejects them as inadequate and even as erroneous.