The work done (in Joule) to compress the piston shown in the figure is defined as:

Where, Pressure, P(s) = k₁ s + k₂

                Area, A = π r²

            Radius, r = 5 x 10^-2 m

            k₁ = 5 x 10⁵ Nm^-3

            k₂ = 10⁵ Nm^-2

            s₀ = 0 m

            s₁ = 5 x 10^-2 m

Now answer the following questions using Matlab:

(a) Create a function file called trap_abc123.mthat (i) takes an input argument n, (ii) calculate the work done by integration using n segment trapezoidal rule and (iii) return the resulting work done.(Note: abc123 is your respective ID)

(b) Create a source file called exam_abc123.mthat calls the function for n = 1, n = 11, n = 21, n = 31, n = 41 and n = 51

(c) Calculate the exact integrationresult using Matlab symbolic tools and calculate the errors in calculating work done for n = 1, n = 11, n = 21, n = 31, n = 41 and n = 51

(d) Plot the work done versus n and error versus n