The Fundamental Theorem of Calculus Section 4.4 Calculus BC AP/Dual, Revised ©2017 viet.dang@humbleisd.net 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Theorems If a function 𝒇 is continuous on 𝒂, 𝒃 and 𝑭 is an antiderivative of 𝒇 on [𝒂, 𝒃], then 𝒂 𝒃 𝒇 𝒙 𝒅𝒙= 𝑭 𝒃 −𝑭 𝒂 The Integral from 𝒂 to 𝒃 of little 𝒇 of 𝒙 is equal to Big 𝑭 of 𝑩 minus Big 𝑭 of 𝑨 which gives the area underneath the curve. If little 𝒇 is positive and BIG 𝑭 is the antiderivative 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
Fundamental Theorem of Calculus §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Example 1 Solve 𝟏 𝟐 𝒙 𝟐 −𝟑 𝒅𝒙 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Example 2 Solve 𝟎 𝟏 𝒙− 𝒙 𝟒 𝒅𝒙 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Example 2 Solve 𝟎 𝟏 𝒙− 𝒙 𝟒 𝒅𝒙 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Your Turn Solve 𝟏 𝟒 𝟑 𝒙 𝒅𝒙 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Example 3 Solve 𝟎 𝟐 𝟐𝒙−𝟏 𝒅𝒙 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Example 3 Solve 𝟎 𝟐 𝟐𝒙−𝟏 𝒅𝒙 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Example 4 Solve 𝟏 𝟒 𝟑− 𝒙−𝟑 𝒅𝒙 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Example 4 Solve 𝟏 𝟒 𝟑− 𝒙−𝟑 𝒅𝒙 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Your Turn Solve 𝟎 𝟑 𝒙 𝟐 −𝟒 𝒅𝒙 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Example 5 Find the area of the region bounded by 𝒚=𝟐 𝒙 𝟐 −𝟑𝒙+𝟐, the 𝒙-axis, 𝒙=𝟎, and 𝒙=𝟐. 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Example 6 Solve 𝟎 𝝅/𝟒 𝐬𝐞𝐜 𝟐 𝒙 𝒅𝒙 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Your Turn Solve 𝟎 𝝅/𝟐 𝐬𝐢𝐧 𝒙+𝟑 𝐜𝐨𝐬 𝒙 𝒅𝒙 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
AP Multiple Choice Practice Question 1 (non-calculator) Solve 𝟏 𝟐 𝟏 𝒙 𝟑 𝒅𝒙 (A) − 𝟕 𝟖 (B) − 𝟑 𝟖 (C) 𝟏𝟓 𝟔𝟒 (D) 𝟑 𝟖 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
AP Multiple Choice Practice Question 1 (non-calculator) Solve 𝟏 𝟐 𝟏 𝒙 𝟑 𝒅𝒙 Vocabulary Process and Connections Answer 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus
§4.4: The Fundamental Theorem of Calculus Assignment Page 288 5-21 EOO, 23-43 odd 4/28/2019 2:06 AM §4.4: The Fundamental Theorem of Calculus