Calculate the exact integration result using matlab

Question

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

W= _s0∫^snP(s)Ads

Where, Pressure, P(s) = k₁ s + k₂
Area, A = πr²

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:

Create a function file called trap_abc123.m that (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)

Create a source file called exam_abc123.m that calls the function for n = 1, n = 11, n = 21, n = 31, n = 41 and n = 51

Calculate the exact integration result 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

Plot the work done versus n and error versus n