 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/discrete-mathematics-continuous-mathematics-and-probability/6/a/i/solution

h = 1/ N

and nodes

x_{j} = j / N

T_{N} = \frac{1}{N} [\frac{1}{2} + j = 1 \sum N - 1 \frac{1}{1 + ( j / N ) ^{2}} + \frac{1}{4}] = \frac{3}{4 N} + j = 1 \sum N - 1 \frac{N}{N ^{2} + j ^{2}}, I \approx T_{N} .

The endpoint weights are half the interior weights, and the endpoint values are

1

and

1/2

 New to topics? Read the docs here!