APM3715 Assignment 1 Complete Solutions UNISA 2025 Numerical Methods for Civil Engineers A - APM3715 Due date 16 May 2025

APM3715
Numerical Methods for Civil
Engineers A - APM3715
ASSIGNMENT 1
FULL SOLUTIONS
UNISA
2025
Assessment 1 (Due: Friday, 16 May
2025)
NAME: ________________________________
STUDENT NUMBER: ___________________
Page 1 of 58

,SOLUTION to Question 1 Part 1.:

1. Let n = 0 :
1 1
𝐼𝑛 = ∫0 𝑒 𝑥 𝑥 𝑛 𝑑𝑥
𝑒

Exact Value Calculation:
1 1 1 1
𝐼0 = ∫0 𝑒 𝑥 𝑑𝑥 = [𝑒1 − 𝑒 0 ] = [𝑒 − 1] = 0.6321206
𝑒 𝑒 𝑒



Page 2 of 58

,SOLUTION to Question 1 Part 1.:




Recurrence Relation Approach:
1
𝐼0 = 1 − = 0.6321206
𝑒



Relative Error:


|𝐸𝑥𝑎𝑐𝑡 𝑉𝑎𝑙𝑢𝑒−𝑅𝑒𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑒 𝑉𝑎𝑙𝑢𝑒|
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝐸𝑟𝑟𝑜𝑟 = |𝐸𝑥𝑎𝑐𝑡 𝑉𝑎𝑙𝑢𝑒|



|0.6321206−0.6321206|
=
0.6321206

= 0.00




Page 3 of 58

, SOLUTION to Question 1 Part 1.:

Let n = 1:
1
1
𝐼𝑛 = ∫ 𝑒 𝑥 𝑥 𝑛 𝑑𝑥
𝑒
0

Exact Value Calculation:
1
1
𝐼1 = ∫ 𝑒 𝑥 𝑥𝑑𝑥
𝑒
0
1
= [𝑥𝑒 𝑥 − 𝑒 𝑥 ] from 0 to 1
𝑒
1
= [1. 𝑒1 − 𝑒1 − (−1)]
𝑒


1
= ≈ 0.3678794
𝑒




Page 4 of 58