Description
Theoretical assignment Consider the following function
f(x) = exp(x) − exp(-x)
exp(x) + exp(-x)
+ ln(x)
wherex ∈ [1, 5]. Use 5 nodes to uniformly cut the interval [1, 5] into 4 subintervals.
1. Note:
(a) Truncate all numbers to 4 decimal places (5 pts).
(b) Please submit only one single file (Pdf or word), including all the
results (5 pts).
(c) In the solution file,
i. for Q2 and Q3, students can refer Pages 4-5 on the slides-lecture
16.
ii. for Q4, students can refer Page 25 on the slides-lecture 16.
2. Use Trapezoid rule to approximate R 5
1
f(x)dx. (20 pts)
3. Use Simpson’s rule to approximate R 5
1
f(x)dx. (20 pts)
4. Use 2 Gaussian points (n = 1) to evaluate the integration in each subinterval, and sum them up to get the integration over the entire domain.
(50 pts)
1
