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MAT3700 Assignment 4 Answers Year 2024

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Mathematics III (Engineering)

Assignment 04 Answers

Year 2024

,
, ANSWERS



1. 𝑓(𝑡) = 𝑡 2 + 𝑡, −𝜋<𝑡<𝜋


1 𝜋
𝑎0 = ∫ 𝑓(𝑡) 𝑑𝑡
𝜋 −𝜋

1 𝜋 2
= ∫ (𝑡 + 𝑡)𝑑𝑡
𝜋 −𝜋

1 𝑡3 𝑡2 𝜋
= [ + ]
𝜋 3 2 −𝜋

1 𝜋3 𝜋2 (−𝜋)3 (−𝜋)2
= [( + ) − ( + )]
𝜋 3 2 3 2

1 𝜋3 𝜋2 𝜋3 𝜋2
= [ + + − ]
𝜋 3 2 3 2

1 2𝜋 3 2𝜋 2
= . =
𝜋 3 3
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