Mathematics III (Engineering)
Assignment 01 Answers
Year 2026
0027 68 628 1800
,
, QUESTION 1
𝑑𝑦
cos(𝑦) = 3𝑥 2 sin(𝑥 3 )
𝑑𝑥
∫ cos(𝑦)𝑑𝑦 = ∫ 3𝑥 2 sin(𝑥 3 ) 𝑑𝑥
sin(𝑦) = ∫ 3𝑥 2 sin(𝑥 3 ) 𝑑𝑥 … … … … … … … (1)
For the integral: ∫ 3𝑥 2 sin(𝑥 3 ) 𝑑𝑥
𝐿𝑒𝑡 𝑢 = 𝑥 3 𝑑𝑢 = 3𝑥 2 𝑑𝑥
∫ 3𝑥 2 sin(𝑥 3 ) 𝑑𝑥 = ∫ sin(𝑢)𝑑𝑢
∫ 3𝑥 2 sin(𝑥 3 ) 𝑑𝑥 = − cos(𝑢) + 𝑐 𝑏𝑢𝑡 𝑢 = 𝑥 3
∫ 3𝑥 2 sin(𝑥 3 ) 𝑑𝑥 = − cos(𝑥 3 ) + 𝑐
From equation 1:
sin(𝑦) = − cos(𝑥 3 ) + 𝑐
𝒚 = 𝒔𝒊𝒏−𝟏 (− 𝐜𝐨𝐬(𝒙𝟑 ) + 𝒄)
Assignment 01 Answers
Year 2026
0027 68 628 1800
,
, QUESTION 1
𝑑𝑦
cos(𝑦) = 3𝑥 2 sin(𝑥 3 )
𝑑𝑥
∫ cos(𝑦)𝑑𝑦 = ∫ 3𝑥 2 sin(𝑥 3 ) 𝑑𝑥
sin(𝑦) = ∫ 3𝑥 2 sin(𝑥 3 ) 𝑑𝑥 … … … … … … … (1)
For the integral: ∫ 3𝑥 2 sin(𝑥 3 ) 𝑑𝑥
𝐿𝑒𝑡 𝑢 = 𝑥 3 𝑑𝑢 = 3𝑥 2 𝑑𝑥
∫ 3𝑥 2 sin(𝑥 3 ) 𝑑𝑥 = ∫ sin(𝑢)𝑑𝑢
∫ 3𝑥 2 sin(𝑥 3 ) 𝑑𝑥 = − cos(𝑢) + 𝑐 𝑏𝑢𝑡 𝑢 = 𝑥 3
∫ 3𝑥 2 sin(𝑥 3 ) 𝑑𝑥 = − cos(𝑥 3 ) + 𝑐
From equation 1:
sin(𝑦) = − cos(𝑥 3 ) + 𝑐
𝒚 = 𝒔𝒊𝒏−𝟏 (− 𝐜𝐨𝐬(𝒙𝟑 ) + 𝒄)
