AP Calculus BC October 11, 2016.

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Presentation transcript:

AP Calculus BC October 11, 2016

Entry Task 𝑥+7 𝑑𝑥 𝑥+6 𝑥 𝑑𝑥 sec 𝑦 tan 𝑦 − sec 𝑦 𝑑𝑦 Find the indefinite integral: 𝑥+7 𝑑𝑥 𝑥+6 𝑥 𝑑𝑥 sec 𝑦 tan 𝑦 − sec 𝑦 𝑑𝑦

Learning Targets I understand the definition of a Riemann Sum I understand how to evaluate a definite integral using limits and properties of definite integrals I can evaluate definite integrals.

Evaluating Definite Integrals Find the integral: −2 1 2𝑥 𝑑𝑥 Area under the curve

Area of common geometric figures 1 3 4 𝑑𝑥 0 3 𝑥+2 𝑑𝑥 −2 2 4− 𝑥 2 𝑑𝑥

Properties of Definite Integrals 𝜋 𝜋 sin 𝑥 𝑑𝑥 = ? 3 0 𝑥+2 𝑑𝑥= ? − 0 3 𝑥+2 𝑑𝑥 = ? −2 0 𝑥 2 𝑑𝑥 + 0 2 𝑥 2 𝑑𝑥 = ? −2 2 𝑥 2 𝑑𝑥= ?

Properties of Definite integrals 2 4 4 𝑥 2 𝑑𝑥 = ? 4 2 4 𝑥 2 𝑑𝑥 = ? 1 3 − 𝑥 2 +4𝑥 −3 𝑑𝑥 = ?

Homework #17 §4.3 #44, 47, 48, 52