Text Book: - Taylor & Menon:
Page 539 following questions need solutions.
1, 2, 3 & 4
Please see attached pages.
The definite integral of a real valued function can be formally defined to be the supremum of all lower sums, or the infimum of all upper sums, provided these two quantities are equal. The solution consists of an attachment just over 1 page in length, written in Word with Mathtype, answering a total of 5 questions involving the use of this formal definition. Each step is explained in the solution using the notation and results given in the attachments to the question (so the reader will need to read these first, and refer to them whilst reading the solutions)