You are working as an apprentice engineer at a company involved in the research, design production and maintenance of bespoke engineering solutions for larger customers. Vocational Scenario or Context Part of your apprenticeship is to spend time working in all departments, however a certain level of understanding needs to be shown before the managing director allows apprentices into the design team and so she has developed a series of questions on integration to determine if you are suitable. Task 1 1 The tasks are to: a) Find the indefinite integral of the function y=3t'+2e3+-+2cos3t b) Calculate the definite integral 317+2e3+4+2cos3t dt 2 An object is moving, such that a=~ +t Determine the functions for: a) Velocity vms ) (integral of acceleration) b) Displacement s m) (integral of velocity) c) Calculate the values of v and s for: i) t=2s ii) t=5s (The constant of integration can be ignored for this question.) 3 Find [ 5 xsin 3 x)dx using the method of integration by P Pears parts