Natural Base Integration Section 5.4 Calculus AP/Dual, Revised ©2017 viet.dang@humbleisd.net 2/22/2019 9:02 PM §5.4: Natural Base Integration
§5.4: Natural Base Integration Guess The Rule 𝒆 𝟐𝒙 𝒅𝒙 2) 𝒆 𝟏 𝟒 𝒙 𝒅𝒙 3) 𝒙 𝒆 𝒙 𝟐 𝒅𝒙 4) 𝐜𝐨𝐬𝒙 𝒆 𝐬𝐢𝐧𝒙 𝒅𝒙 5) 𝒆 𝟏/𝒙 𝒙 𝟐 𝒅𝒙 6) 𝒆 𝒖 𝒅𝒖 2/22/2019 9:02 PM §5.4: Natural Base Integration
Antiderivatives of Natural Base 𝒆 𝒖 𝒅𝒖= 𝒆 𝒖 +𝑪 Use 𝒖-substitution to solve 2/22/2019 9:02 PM §5.4: Natural Base Integration
§5.4: Natural Base Integration Example 1 Solve 𝒆 𝟑𝒙+𝟏 𝒅𝒙 2/22/2019 9:02 PM §5.4: Natural Base Integration
§5.4: Natural Base Integration Example 2 Solve 𝟓𝒙𝒆 − 𝒙 𝟐 𝒅𝒙 2/22/2019 9:02 PM §5.4: Natural Base Integration
§5.4: Natural Base Integration Your Turn Solve 𝒙 𝟐 𝒆 𝒙 𝟑 𝟐 𝒅𝒙 2/22/2019 9:02 PM §5.4: Natural Base Integration
§5.4: Natural Base Integration Example 3 Solve 𝒆 𝟐𝒙 𝟏+ 𝒆 𝟐𝒙 𝒅𝒙 2/22/2019 9:02 PM §5.4: Natural Base Integration
§5.4: Natural Base Integration Example 4 Solve 𝐬𝐢𝐧 𝒙 𝒆 𝐜𝐨𝐬 𝒙 𝒅𝒙 2/22/2019 9:02 PM §5.4: Natural Base Integration
§5.4: Natural Base Integration Example 5 Solve 𝟐 𝒆 𝒙 −𝟐 𝒆 −𝒙 𝒆 𝒙 + 𝒆 −𝒙 𝟐 𝒅𝒙 2/22/2019 9:02 PM §5.4: Natural Base Integration
§5.4: Natural Base Integration Example 6 Solve −𝟐 𝟎 𝒙 𝟐 𝒆 𝒙 𝟑 𝒅𝒙 2/22/2019 9:02 PM §5.4: Natural Base Integration
§5.4: Natural Base Integration Example 6 Solve −𝟐 𝟎 𝒙 𝟐 𝒆 𝒙 𝟑 𝒅𝒙 2/22/2019 9:02 PM §5.4: Natural Base Integration
§5.4: Natural Base Integration Your Turn Solve 𝟑 𝟒 𝒆 𝟑−𝒙 𝒅𝒙 2/22/2019 9:02 PM §5.4: Natural Base Integration
AP Multiple Choice Practice Question 1 (non-calculator) Solve 𝒙 𝟐 𝒆 𝒙 𝟑 𝒅𝒙 (A) − 𝟏 𝟑 𝐥𝐧 𝒆 𝒙 𝟑 + 𝑪 (B) − 𝒆 𝒙 𝟑 𝟑 + 𝑪 (C) − 𝟏 𝟑 𝒆 𝒙 𝟑 + 𝑪 (D) 𝟏 𝟑 𝐥𝐧 𝒆 𝒙 𝟑 + 𝑪 2/22/2019 9:02 PM §5.4: Natural Base Integration
AP Multiple Choice Practice Question 1 (non-calculator) Solve 𝒙 𝟐 𝒆 𝒙 𝟑 𝒅𝒙 Vocabulary Connections and Process Answer and Justifications 2/22/2019 9:02 PM §5.4: Natural Base Integration
§5.4: Natural Base Integration Assignment Page 354 91-117 odd 2/22/2019 9:02 PM §5.4: Natural Base Integration