Calculus Unit 8

Big Idea:

Integrals and The Fundamental Theorem of Calculus

Student Expectations:

Focus Standard

EU 3.4: The definite integral of a function over an interval is a mathematical tool with many interpretations and applications involving accumulation.

• EK 3.4A1: A function defined as an integral represents an accumulation of a rate of change.
• EK 3.4A2: The definite integral of the rate of change of a quantity over an interval gives the net change of that quantity over that interval.
• EK 3.4B1: The average value of a function over an interval is
• EK 3.4C1: For a particle in rectilinear motion over an interval of time, the definite integral of velocity represents particle’s displacement over the interval of time and the definite integral of speed represents the particle’s total distance traveled over the interval of time.
• EK 3.4C2: (BC) The definite integral can be used to determine the displacement, distance, and position of a particle moving along a curve given by parametric or vector-valued functions.
• EK 3.4D1: Areas of certain regions of the plane can be calculated with definite integrals.
• EK 3.4D2: Volumes of solids with known cross sections, including disks and washers, can be calculated with definite integrals.
• EK 3.4D3: (BC) The length of a planar curve defined by a function or by a parametrically defined curve can be calculated using a definite integral.
• EK 3.4E1: The definite integral can be used to express information about accumulation and net change in many contexts.

Student Learning Targets:

• I will interpret the meaning of a definite integral within a problem
• I will apply definite integrals to problems involving average value of a function
• I will apply definite integrals to problems involving motion
• I will apply definite integrals to problems involving area and volume
• I will apply definite integrals to problems involving length of a curve (BC)
• i will use the definite integral to solve problems in various contexts

Essential Questions:

Extra Information:

Adopted Textbook:

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