Question

Use the driven equation x (t) from (C) and solve it using the following

numerical methods over the time interval 0 ≤ t ≤ 3 seconds at h=0.5.

I. Using the trapezium method

II. Using a Simpsons rule

Answer 1

Let the driven equation be -

$x(t)=3t^2+2$

(i) Trapezoidal rule-

$=\int_0^3 (3t^2+2) dt$ and h=0.5 assuming n=3

The values are-

$\int_0^3 (3t^2+2)dt=\dfrac{h}{2}(2+2.75+5+8.75)\\[9pt] =\dfrac{1.5}{2}\times 18.5 \\[9pt] =13.875$

Hence $\int_0^3 (3t^2+2) dt=13.875$

(ii) Using Simpson's rule-

    $=\int_0^3 (3t^2+2)dt\\[9pt]=\dfrac{3t^3}{3}+2t|_0^3\\[9pt]=(27-0)+(2(3-0)=33$