Problems about Numerical Approximations of Integrals

1
Problems about Numerical Approximations of
Integrals
2
Compare RIGHT(n) and LEFT(n)
Problem
Solution
Graphical solution to the same problem is on the
next page.
3
Compare RIGHT(n) and LEFT(n)
Problem
Solution
4
Compare TRAP(n) and LEFT(n)
Problem
Solution
5
Compare MID(n) and LEFT(2n)
Problem
Solution
The picture below shows the interval a,b
divided into 2n subintervals. The crossed points
are the left end-points of subintervals in a
division of a,b into n subintervals. The
circled points are the mid-points of the
subintervals (for which the crossed points are
the left end-points). Points which are either
circled or crossed are left end-points of
subintervals of a division of a,b into 2n
subintervals.