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
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
