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MAT3700 Assignment 01 Answers Year 2025

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MAT3700-Mathematics III (Engineering) Assignment 01 Answers with clear step by step calculations. Distinction Guaranteed

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Mathematics III (Engineering)

Assignment 01 Answers

Semester 1 2025




0027 63 985 5033

,
,QUESTION 1.

𝑑𝑦
cos 𝑦 = 2 𝑠𝑖𝑛2 𝑥 cos 𝑥
𝑑𝑥

∫ cos 𝑦 𝑑𝑦 = 2 ∫ 𝑠𝑖𝑛2 𝑥 cos 𝑥 𝑑𝑥


sin 𝑦 = 2 ∫ 𝑠𝑖𝑛2 𝑥 cos 𝑥 𝑑𝑥


For the integral

∫ 𝑠𝑖𝑛2 𝑥 cos 𝑥 𝑑𝑥 𝑙𝑒𝑡 𝑢 = sin 𝑥 𝑑𝑢 = cos 𝑥


∫ 𝑠𝑖𝑛2 𝑥 cos 𝑥 𝑑𝑥 = ∫ 𝑢2 𝑑𝑢


1
= 𝑢3 + 𝑐
3

1
= 𝑠𝑖𝑛3 𝑥 + 𝑐
3
1
sin 𝑦 = 2 ( 𝑠𝑖𝑛3 𝑥 + 𝑐)
3

2
𝑦 = arcsin ( 𝑠𝑖𝑛3 𝑥 + 2𝑐) 𝑙𝑒𝑡 2𝑐 = 𝐴
3

𝟐
𝒚 = 𝐚𝐫𝐜𝐬𝐢𝐧 ( 𝒔𝒊𝒏𝟑 𝒙 + 𝑨)
𝟑

, QUESTION 2.



𝑑𝑦
(𝑥 3 + 𝑦 3 ) = 3𝑥𝑦 2
𝑑𝑥
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