g=0.6 h=400. k=-1.415

6) Integrate a) f(5t3 + g)dt b) f0! e'm" + 4 cos(2x))dx 7) The area under the force-displacement (Rx) graph of a spring under compression represents the work done in compressing the spring. .9 Work done = f F dx 0 If the force F required to compress a rubber spring is given by F = 7.5x + 120x3 Newtons where x is the displacement from its resting position. Calculate the work done in compressing the spring from rest by a displacement of g metres HE04ilssue 6fJune 2022 8) In an AC signal processing circuit, the mean voltage of a half wave rectier over a time period T is given by me = 1% for 1: sin (100m) dt Calculate the mean voltage over a time period T of 0.0045. 9) In a spark ignition engine, a mixture of air and petrol vapour is compressed in a cylinder starting at a volume V of me = 0.04 m3 to a volume of Vend = 0.008 m3. The work done in moving the piston is given by 0. 008 Work done = - I P (it! where P is the Pressure 0.04 If the fuelair mixture behaves as a polytropic uid under compression and obeys the power law relationship P= 47Vk determine the work done by the piston. 10) When a bearing fails in a vertical boring machine, the rate of temperature rise is observed to be where the temperature T is measured in Kelvin and time c is measured in seconds The initial temperate of the hearing at the moment of failure was recorded as 298 K (25C). By using an appropriate integration method give the equation that describes the temperature T in terms of the time t