Distance vs. Displacement & Properties of Integrals

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Distance vs. Displacement & Properties of Integrals AP Calculus December 6, 2016 Mrs. Agnew

Free powerpoint template: www.brainybetty.com Essential Question How do you find the distance and displacement of an object given a velocity curve? How do you use the properties of integrals? Essential Vocabulary Distance vs. Displacement Properties of Definite Integrals Limits of Integration Free powerpoint template: www.brainybetty.com

Free powerpoint template: www.brainybetty.com Review: Integration The definite integral gives the following: Area Under a Curve Total Change Evaluation Theorem: find antiderivative and plug in limits of integration. Free powerpoint template: www.brainybetty.com

Distance vs. Displacement Assuming velocity is always positive, area under the curve is the Total Distance. If velocity is both positive and negative, area under curve is Displacement. Free powerpoint template: www.brainybetty.com

Distance vrs. Displacement Displacement is given by the area under the velocity curve. Distance is area under curve, making any negative area positive (examine graph). Guided Practice Free powerpoint template: www.brainybetty.com

Properties of the Definite Integral Free powerpoint template: www.brainybetty.com

Free powerpoint template: www.brainybetty.com Guided Practice Page 279 #33 – 44 Page 296 #97 – 103 (Odd) Free powerpoint template: www.brainybetty.com