Calculus Unit 10

Big Idea:

Integrals and the Fundamental Theorem of Calculus

Student Expectations:

Focus Standards

EU 3.3: The Fundamental Theorem of Calculus, which has two distinct formulations, connects differentiation and integration.

• EK 3.3B5: Techniques for finding antiderivatives include algebraic manipulation such a long division and completing the square, substitution of variables, (BC) integration by parts, and non repeating linear partial Fractions.

EU 3.5: Antidifferentiation is an underlying concept involved in solving separable differential equations. Solving separable differential equations involves determining a function or relation given its rate of change.

• EK 3.5A1: Antidifferentiation can be used to find specific solutions to differential equations with given initial conditions, including applications to motion along a line, exponential growth and decay, (BC) and logistic growth.
• EK 3.5B2: (BC) The model for logistic growth that arises from the statement “The rate of change of a quantity is jointly proportional to the size of the quantity and the difference between the quantity and the carrying capacity “ is .

Student Learning Targets:

• I will calculate antiderivatives
• I will evaluate definite integrals
• I will analyze differential equations to obtain general and specific solutions
• I will interpret, create, and solve, differential equations from problems in context.

Essential Questions:

Extra Information:

Adopted Textbook:

District Grading Policy

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