show working out please

b) For the second example the current in a circuit is related to time by the following equation: 8 5 sin(2t) + 3 Hint: Q = It where Q =charge, I =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.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.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 Plot a graph of v (vertical) against t (horizontal) and show on it what represents the displacement covered between 5 seconds and 12 seconds.1) In order to help you brush up on your basic Differential skills Ivelisse would like you to differentiate the three following equations with respect to x a) y = 4. 5x + 3. 2x - 2. 8x + 5 dy = dx 3.5x b) y = 2. 4e + 3x dy = dx () y = 2sin(3x) + 4cos(2. 5x) dy dx 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 - 5.6 dx = e) 5sin(2x) - 3e dx =