Section 4.2A Calculus AP/Dual, Revised ©2018

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Section 4.2A Calculus AP/Dual, Revised ©2018 viet.dang@humbleisd.net Trapezoidal Area Section 4.2A Calculus AP/Dual, Revised ©2018 viet.dang@humbleisd.net 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

Review Find the area of the trapezoid. 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

Trapezoidal Area (Uneven Area) Find the area of the curve using the trapezoid sum. 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

Trapezoidal Rule To evaluate a definite integral involving a function whose anti-derivative cannot be found Integral: 𝒂 𝒃 𝒇 𝒙 𝒅𝒙 = 𝟏 𝟐 𝒃−𝒂 𝒏 𝑳 𝒏 + 𝑹 𝒏 Area of Trapezoidal Rule: 𝟏 𝟐 𝒙 𝒇 𝒙 𝟎 +𝒙𝟏 +𝒇 𝒙 𝟏 +𝒙𝟐 +…+𝒇 𝒙 𝒏−𝟏 +𝒙𝒏 𝒙= 𝒃−𝒂 𝒏 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

Example 1 Use the Trapezoidal Rule to approximate the value of 𝟏 𝟓 𝒙 𝟐 +𝟑 𝒅𝒙 for 𝒏=𝟒. 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

Example 1 Use the Trapezoidal Rule to approximate the value of 𝟏 𝟓 𝒙 𝟐 +𝟑 𝒅𝒙 for 𝒏=𝟒. 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

Example 1 Use the Trapezoidal Rule to approximate the value of 𝟏 𝟓 𝒙 𝟐 +𝟑 𝒅𝒙 for 𝒏=𝟒. Solve using FTC: 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

Example 2 Use the Trapezoidal Rule to approximate the value of 𝟏 𝟑 𝟒−𝒙 𝟐 𝒅𝒙 for 𝒏=𝟒. 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

Your Turn Use the Trapezoidal Rule to approximate the value of 𝟏 𝟗 𝒙 𝟐 𝒅𝒙 for 𝒏=𝟒. 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

Review Use the Left Hand Sum to approximate the value of 𝟏 𝟕 𝒇 𝒙 𝒅𝒙 . 𝟐 𝟓 𝟔 𝟕 𝒇 𝒙 𝟑 −𝟏 𝟒 𝟖 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

Example 3 Use the Trapezoidal Rule to approximate the value of 𝟏 𝟕 𝒇 𝒙 𝒅𝒙 𝒙 𝟏 𝟐 𝟓 𝟔 𝟕 𝒇 𝒙 𝟑 −𝟏 𝟒 𝟖 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

Your Turn Use the Trapezoidal Rule to approximate the value of 𝟏 𝟏𝟑 𝒇 𝒙 𝒅𝒙 . 𝒙 𝟏 𝟑 𝟖 𝟏𝟐 𝟏𝟑 𝒇 𝒙 𝟐 𝟓 𝟒 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

AP Multiple Choice Practice Question 1 (non-calculator) The graph of 𝒇 is shown below. Approximate 𝟐 𝟏𝟐 𝒇 𝒙 𝒅𝒙 using the trapezoid approximation. (A) 𝟒𝟒 (B) 𝟖𝟖 (C) 𝟏𝟏𝟐 (D) 𝟐𝟐𝟒 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

AP Multiple Choice Practice Question 1 (non-calculator) The graph of 𝒇 is shown below. Approximate 𝟐 𝟏𝟐 𝒇 𝒙 𝒅𝒙 using the trapezoid approximation. Vocabulary Process and Connections Answer 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum

Assignment Worksheet 2/25/2019 7:22 AM §4.2A: Trapezoidal Sum