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How is integral calculus used to help solve real world problems found in physics, biology, economics, and other applications?
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Student Learning Map
- Topic:Applications of Definite Integrals
- Subject(s):Math
- Days:30
- Grade(s):11, 12
Key Learning:
To use integrals and derivatives to find velocities from acceleration relationships, solve separable differential equations, find areas and volumes, and model and solve problems in physics, biology, and economics.
Unit Essential Question(s):
Concept: Exponential Growth and Decay, and Areas in the Plane Lesson Essential Question(s):How are integrals and derivatives used to solve exponential growth and decay problems? (A)How are integrals and derivatives used to solve exponential growth and decay problems? (ET)How are integrals used to calculate areas between a curve and the x-axis and y-axis? (A)How are integrals used to calculate the area between two curves? (A)Vocabulary:Vocabulary:Vocabulary:
Additional Info:
Calculus textbook Graphing Calculator TI-Presenter Ancillary material
Resources:
Acquisition Lesson(s):
1. How are integrals and derivatives used to solve exponential growth and decay problems?2. How are integrals used to find the volume of a solid with a known cross-sectional area?3. How are derivatives and integrals used to model and solve problems in physics, biology, and economics?4. How are integrals used to calculate areas between a curve and the x-axis and y-axis?5. How are integrals used to calculate the area between two curves?6. How are derivatives and integrals used to calculate the length of curves?Extended Thinking Lesson(s):
1. How are integrals and derivatives used to solve exponential growth and decay problems?2. What are additional applications of derivatives and integrals?3. How is the relationship between derivatives and integrals benefical is solving other application problems?