Decision 6: Acquisition Lesson:
Title:
How are derivatives and integrals used to calculate the length of curves?
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?