Evaluate the following integrals: i. ∫4(1−−43 +25) 0 ii. ∫3(2) 0 a) Analytically b) Multiple application of Trapezoidal rule n = 4. c) Simpson’s 1/3 rule for n = 4. d) Simpson’s 1/3 and Simpson’s 3/8 rule for n = 5. e) Determine the true percent relative error.

The thermal expansion or contraction of a given metal is a function of the f a)-density b)-initial temperature c)- temperature difference d)- linear coefficient of thermal expansion e)- final temperature f)- original length

Assuming compressible flow of air and that the measurements are done at flagstaff a pitot static tube that gives the difference of total and static pressure measures 0.35 m of mercury. what is the velocity of air? assume the temperature to be 300k. (submit your excel or matlab calculation sheet)

Derive the correction factor formula for conical nozzle i=-(1+ cosa) and calculate the nozzle angle correction factor for a nozzle whose divergence hal-fangle is 13 (hint: assume that all the mass flow originates at the apex of the cone.