APM3715 Assignment 01 Answers Year 2025

Numerical Methods for Civil Engineers

Assignment 01 Answers

Year 2025




0027 63 985 5033

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QUESTION 1

The exact values are calculated as follows;

1 1
𝐼𝑛 = ∫ 𝑒 𝑥 𝑥 𝑛 𝑑𝑥
𝑒 0

1 1 𝑒−1
𝑒. 𝑔 𝐼0 = ∫ 𝑒 𝑥 𝑥 0 𝑑𝑥 = = 0.63212055883
𝑒 0 𝑒



The recurrence values are calculated as follows;
1
𝐼0 = 1 − = 0.63212055883
𝑒
𝐼𝑛 = 1 − 𝑛𝐼𝑛−1 𝑒. 𝑔 𝐼1 = 1 − (1 × 0.63212055883) = 0.3678794412


Relative error is given by

|𝐼𝑛𝑒𝑥𝑎𝑐𝑡 − 𝐼𝑛𝑟𝑒𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑒 |
𝑅. 𝐸 = × 100
|𝐼𝑛𝑒𝑥𝑎𝑐𝑡 |


n Exact Value Recurrence Value Relative Error (%)
0 0.6321206 0.6321206 0.00
1 0.3678794 0.3678794 0.00
2 0.2642411 0.2642411 0.00
3 0.2072766 0.2072766 0.00
4 0.1708934 0.1708934 0.00
5 0.1455329 0.1455329 0.00
6 0.1268024 0.1268024 0.00

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