How do you use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n=6 for #int 9 sqrt (ln x) dx# from [1,4]?
1 Answer
See the explanation section, below.
Explanation:
For this question we have
For all three approximations, we have
(To eveluate
We need the endpoints of the 6 subintervals. Start at
The endpoints of the subintervals are:
Now for the Trapezoidal and Simpson's Rules just apply the formula and do the arithmetic
Trapezoidal:
Simpson's:
Do the arithmetic.
Midpoint rule , needs the midpoints of the subintervals. We'll call them
Do the arithmetic.