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MAT1581 ASSIGNMENT 4 SEMESTER 2 2020 SOLUTIONS. THIS IS PERFECT TOOL TO HELP YOU WITH THE FIRST ASSIGNMENT FOR SECOND SEMESTER AND PREPARE FOR THE FINAL EXAMINATION. THE SOLUTIONS HAVE STEP BY STEP CALCULATIONS AND EXPLANATIONS. CONTACT US FOR CATCH UP CLASSES OR VIDEO EXPLANATIONS

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  • August 13, 2020
  • 6
  • 2020/2021
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MAT1581


SEMESTER 02


2020


ASSIGNMENT 04


MEMO

, Question 1
1.1
3
 ∫ (√𝑥 + ln(𝑒 𝑥 ) + 3𝑥 + 𝑥 5 ) 𝑑𝑥

3
 ∫ √𝑥 𝑑𝑥 + ∫ ln(𝑒 𝑥 )𝑑𝑥 + ∫ 3𝑥 𝑑𝑥 + ∫ 𝑥 5 𝑑𝑥

3 3
2 2
 ∫ √𝑥 𝑑𝑥 = 𝑥 2 × 3 = 3 𝑥 2 + 𝐶

𝑥2
 ∫ ln(𝑒 𝑥 )𝑑𝑥 = ∫ 𝑥 𝑑𝑥 = +𝐶
2

3𝑥
 ∫ 3𝑥 𝑑𝑥 = ln 3
+𝐶

3 3 1 3
 ∫ 𝑥 5 𝑑𝑥 = 𝑥 4 × (− 4) = − 4𝑥 4 + 𝐶

𝟑 𝟐 𝟑 𝒙𝟐 𝟑𝒙 𝟑
 ∫ (√𝒙 + 𝐥𝐧(𝒆𝒙 ) + 𝟑𝒙 + 𝟓) 𝒅𝒙 = 𝒙𝟐 + + − +𝑪
𝒙 𝟑 𝟐 𝐥𝐧 𝟑 𝟒𝒙𝟒


1.2


 ∫ 𝑒 2𝑥+1 𝑑𝑥

 𝑙𝑒𝑡 𝑢 = 2𝑥 + 1

𝑑𝑢 1
 𝑑𝑥
= 2 ; 𝑑𝑥 = 2 𝑑𝑢

 𝑟𝑒𝑝𝑙𝑎𝑐𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑖𝑛𝑡𝑒𝑔𝑟𝑎𝑙
1
 ∫ 𝑒 2𝑥+1 𝑑𝑥 = ∫ 𝑒 𝑢 × 2 𝑑𝑢

1
 ∫ 𝑒 2𝑥+1 𝑑𝑥 = 2 ∫ 𝑒 𝑢 𝑑𝑢

1
 ∫ 𝑒 2𝑥+1 𝑑𝑥 = 2 𝑒 𝑢 + 𝐶

 𝑁𝐵: 𝑢 = 2𝑥 + 1

𝟏
 ∫ 𝒆𝟐𝒙+𝟏 𝒅𝒙 = 𝟐 𝒆𝟐𝒙+𝟏 + 𝑪


1.3

𝑥 2 +3𝑥+5
 ∫ 𝑥+3
𝑑𝑥

 𝑝𝑒𝑟𝑓𝑜𝑟𝑚 𝑙𝑜𝑛𝑔 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛

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