DSC1520 ASSIGNMENT 4 SEMESTER 2 2022

ANSWER
2 3
‫ ׬‬100𝑥 99 + 20𝑥 4 + 𝑥 2 + 𝑥 + 9𝑑𝑥
2 3
‫ ׬‬100𝑥 99 𝑑𝑥 + ‫ ׬‬20𝑥 4 𝑑𝑥 + ‫ 𝑥 ׬‬2 𝑑𝑥 + ‫ 𝑥𝑑 𝑥 ׬‬+ ‫ ׬‬9𝑑𝑥
1 2 3
100 ቀ100 𝑥 100 + 𝑐ቁ + ‫ ׬‬20𝑥 4 𝑑𝑥 + ‫ 𝑥 ׬‬2 𝑑𝑥 + ‫ 𝑥𝑑 𝑥 ׬‬+ ‫ ׬‬9𝑑𝑥

1 1 2 3
100 ቀ100 𝑥 100 + 𝑐ቁ + 20 ቀ5 𝑥 5 + 𝑐ቁ + ‫ 𝑥 ׬‬2 𝑑𝑥 + ‫ 𝑥𝑑 𝑥 ׬‬+ ‫ ׬‬9𝑑𝑥

1 1 3
100 ቀ100 𝑥 100 + 𝑐ቁ + 20 ቀ5 𝑥 5 + 𝑐ቁ + 2 ‫ 𝑥(׬‬2 )−1 𝑑𝑥 + ‫ 𝑥𝑑 𝑥 ׬‬+ ‫ ׬‬9𝑑𝑥

1 1
100 ቀ100 𝑥 100 + 𝑐ቁ + 20 ቀ5 𝑥 5 + 𝑐ቁ + 2 ‫ 𝑥(׬‬2 )−1 𝑑𝑥 + 3(𝐼𝑛ۤ𝑥‫ ۥ‬+ 𝑐 + ‫ ׬‬9𝑑𝑥

𝑥 100 𝑥5
100 ቀ 100 + 𝑐ቁ + 20 ቀ 5 + 𝑐ቁ + 2 ‫ 𝑥 ׬‬−2 𝑑𝑥 + 3(𝐼𝑛 (ȁ𝑥ȁ) + 𝑐 + 9𝑥 + 𝑐

𝑥 100 𝑥5
100 ቀ 100 + 𝑐ቁ + 20 ቀ 5 + 𝑐ቁ + 2(−𝑥 −1 + 𝑐) + 3(ȁ𝑥ȁ + 𝑐) + 9𝑥 + 𝑐
2
∴ 𝑥 100 + 4𝑥 5 − 𝑥 + 3𝐼𝑛(ȁ𝑥ȁ) + 9𝑥 + 𝑐

Option A