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“CALCULUS” – **UNIT 5: Concepts of Integration High School Mathematics “Calculus: Graphical, Numerical, Algebraic” Target Time Frame: OPTIONAL MATERIAL STANDARD A. Recognizing definite integrals as a summation (Reimann Sum) and as the area under a curve (geometric) using rectangular/trapezoidal approximations. B. Find antiderivatives, apply basic integration formulas, and find distance and velocity functions from initial conditions. C. Understand and apply the concepts and properties of definite integrals including the Fundamental Theorem . D. Solve simple first order differential equations, recognize and graph slope fields, and apply first order differential equations to growth and decay problems. E. Integrate functions using u-substitution and integration by parts. ESSENTIAL QUESTION What is a definite integral? DEPTH for MASTERY ALL Sections COMMENTS 5.1, 5.2, 5.5 *This Unit is Optional for non AP Calculus. These topics will be covered if time allows. How do you solve an initial value problem? ALL 6.1 How do you calculate a definite integral? ALL 5.3, 5.4 How can differential equations be used to solve real-world problems? ALL 6.1, 6.2, 6.4 How can you integrate functions using u-substitution and integration by parts? ALL 6.2, 6.3