Update
Questions
Bell Ringer
Review
 Prerequisites
 Derivatives
 Derivative Rules
 Power Rule
 Constant Rule
 Trig Derivatives
 Antiderivative (video)
 Indefinite Integral
 Definition
 Integral Sign
 Integrand
 Variable of Integration
 Constant of Integration
 General Solution
 Basic Integration Rules
 Summation (Sigma Notation) (video)
 Area Under a Curve (video 1) (video 2) (video 3)
 Fundamental Theorem of Calculus
 Definite Integrals
 Integration by Substitution (video 1) (video 2) (video 3)
 How can integration by substitution be used to solve problems?
 Integrate by substitution.
 Checkpoints
Lesson
Exit Ticket
 Lesson Objective(s)
Skills
 Find critical numbers using differentiation.
 Find extrema on a closed interval using differentiation.
 Apply understanding of Rolle’s Theorem and the Mean Value Theorem.
 Determine intervals on which a function is increasing or decreasing.
 Apply the First Derivative Test to find relative extrema of a function.
 Determine intervals on which a function in concave upward or downward.
 Apply the Second Derivative Test to find inflection points of a function.
 Determine horizontal asymptotes using limits.
 Determine finite limits at infinity.
 Determine infinite limits at infinity.
 Determine the conditions that optimize a situation.
 Calculate the antiderivative of a function.
 Calculating the area under a curve using summation.
 Calculate the area under a curve using definite integration.
 Integrate by substitution.
Standard(s)
 APC.10
 Use Riemann sums and the Trapezoidal Rule to approximate definite integrals of functions represented algebraically, graphically, and by a table of values and will interpret the definite integral as the accumulated rate of change of a quantity over an interval interpreted as the change of the quantity over the interval
 Riemann sums will use left, right, and midpoint evaluation points over equal subdivisions.
 APC.11
 The student will find antiderivatives directly from derivatives of basic functions and by substitution of variables (including change of limits for definite integrals).
 APC.12
 The student will identify the properties of the definite integral. This will include additivity and linearity, the definite integral as an area, and the definite integral as a limit of a sum as well as the fundamental theorem.
 APC.13
 The student will use the Fundamental Theorem of Calculus to evaluate definite integrals, represent a particular antiderivative, and facilitate the analytical and graphical analysis of functions so defined.
 APC.14
 The student will find specific antiderivatives, using initial conditions (including applications to motion along a line). Separable differential equations will be solved and used in modeling (in particular, the equation y' = ky and exponential growth).
 APC.15
 The student will use integration techniques and appropriate integrals to model physical, biological, and economic situations. The emphasis will be on using the integral of a rate of change to give accumulated change or on using the method of setting up an approximating Riemann sum and representing its limit as a definite integral. Specific applications will include
 a) the area of a region;
 b) the volume of a solid with known crosssection;
 c) the average value of a function; and
 d) the distance traveled by a particle along a line.
Past Checkpoints  Antiderivative
 Area of a Plane Region
 Fundamental Theorem of Calculus
 Definite Integrals
