A Level Maths Notes: C3 – Applications of Simpson's Rule
Simpson's rule allows approximate calculations of definite integrals that might otherwise not be easily calculable. The approximation is given by
where
the
number of strips, is even. Given an integral to estimate, we draw up
a table of function values
Example: Using Simpson's
Rule with six strips, estimate the value of the integral
|
x_i |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
|
f_i |
1 |
2 |
4 |
8 |
16 |
32 |
64 |
Example: Using Simpson's
Rule with five strips, estimate the to three decimal places the value
of the integral
Find
the percentage error.
Because the final answer is to be to three decimal places, all figures in the working will be to four decimal places. Only the final answer will be to three decimal places.
|
x_i |
0 |
2 |
4 |
6 |
8 |
10 |
12 |
|
f_i |
0 |
1.4142 |
2 |
2.4495 |
2.8284 |
3.1623 |
3.4641 |
to four decimal places so
The true value is
The % error is