clear work out please

ii) Calculate using definite integration the displacement covered between the 5 seconds and 12 seconds of motion. iii) Estimate using a summation method the displacement covered between the 5 seconds and 12 seconds of motion iv) Comment on how the calculated and estimated values compare and the respective ease of use and accuracy of the two methods. b) For the second example the current in a circuit is related to time by the following equation: I = = sin(2t) + 3 Hint: Q = It where Q =charge, / =current, t =time Calculate using definite integration the charge developed in the circuit from 0.2 to 0.7 seconds. ii) Estimate using summation the charge developed in the circuit from 0.2 to 0.7 seconds. iii) Comment on how the calculated and estimated values compare and the respective ease of use and accuracy of the two methods.Assuming you have been able to handle basic differentiation, Ivelisse would like you to check you can complete indefinite integration by completing the following 2 integrals. d) 4x - 6x + 8. 4x - 5.6dx = e) 5sin(2x) - 3edx = Definite integration is use in engineering to determine the area under a graph, as such is particularly useful in velocity time graphs to determine displacement, acceleration time graphs to determine velocity for mechanical systems and in voltage current graphs to determine power and current time graphs to determine charge in electrical systems. 2) To this end Ivelisse would like you practice your definite integration skills and compare them to the alternative of using summation to arrive at the same answer a) For the first example during start-up part of a machine moves with a velocity given by the equation: v = 7t - 0. 8tmm/s i) Plot a graph of v (vertical) against t (horizontal) and show on it what represents the displacement covered between 5 seconds and 12 seconds.To gain further experience with your company, you have now been moved into the department that designs electronic equipment. The job you are currently working on is helping to design racking systems for the PS50 power supply unit. Power supplies have special circuits in them to smooth out any irregularities in the DC output voltage and because you are training to be a composite engineer your knowledge of electronic circuits is limited. As you are keen to find out more about power supplies you decide to talk to a colleague, Ivelisse a Senior Engineer in the department. She tells you that an important component in any smoothing circuit is its capacitor and the best way to find out how one works is to model its operation using mathematics. Before trying to do this Ivelisse recommends that you brush up on your knowledge of differential and integral calculus. Where calculations are involved, express your answers accurate to three decimal places (d.p.) and carry out checks on your solutions