d) For a function p(t) which describes the change in probability that a light bulb burns out at time t, the integral / p(t) dt.Problem 6: For each of the following scenarios, explain what the amiated integral represents. a) For a function t(m) which describes the change in temperature in a cooling mug of tea over 111 ('3 minutes1 the integral 1 than!) dm. 1'] b) For a. function C(b) which describes the change in cost of producing (3 books, the integral 150 f (:(b) db. 100 e) For a function 3(1)) which describes the change in size of a population of animals after 1; years, the integral f 3(y) dy. 4 b) Regardless of your answer to part a), how do you think the concepts of continuity and differen- tiability relate to the integral of a function, if at all?Problem 8: Answer the following questions about integrals and differentiability. a) When we learned about differentiation, we discovered that there are numerous functions for which their derivatives don't exist. Do you think it is possible to have a function whose integral doesn't exist? Why or why not? Write at least a paragraph explaining your reasoning