Question

#5) (Please be as clear as possible in your answer and write as big and neatly as possible so the answer is easily visible and easy to read)

a) The following table gives the values of a function f(x) at a certain number of equidistant points on the x-axis. From the data supplied, calculate approximate values of  by using each of the following rules: (Give the explicit formula/definition for each of the rules, before applying them)

(i) The Trapezoid Rule and (ii) Simpson's Rule.

x =	0.0	0.2	0.4	0.6	0.8	1.0	1.2	1.4	1.6	1.8	2.0
f (x) =	2.7	2.1	2.3	1.7	2.2	2.9	3.1	3.4	3.9	4.9	8.7

b) Use the Midpoint Rule to find the approximation  to 6 decimal places.

Answer 1

(i)

Trapezoidal rule:

we can use formula

we can plug values

........Answer

(ii)

Simpson's rule:

we can use formula

now, we can plug values

(b)

Left sum:

Right Sum:

Mid-point sum:

.........Answer