Integration using Substitution (Topics 6.9)
Unit 6  Day 15
Unit 6
Day 1
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Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
Day 10
Day 11
Day 12
Day 1314
Day 15
Day 16
Day 17
Day 18
Day 19
Day 20
Day 21
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Learning Objectives

Use usubstitution to find antiderivatives of composite functions
Success Criteria

I can determine when usubstitution is necessary for evaluating a definite integral

I can evaluate a definite integral using usub

I can rewrite the limits of integration when doing usubstitution
Quick Lesson Plan
Overview
Today’s Scavenger Hunt provides engaging practice with usubstitution. Students work in groups to solve eleven integrals, using the answer of each problem to locate the next station.
Teaching Tips
Prior to the Scavenger Hunt, as a warmup activity, our students were presented with a definite integral which required substitution techniques. We allowed students to evaluate their integral and then encouraged them to confirm their result with NINT (Math:9) on their calculators. Those students who used integrands written in terms of u  but evaluated with limits in terms of x  were surprised to discover a discrepancy in their results. It is critical that students understand the source of the discrepancy.
The multiplechoice options on the Scavenger Hunt include answers obtained by common mistakes and many incorrect answers will be attractive to students. Teachers should move among the groups during this activity to ask guiding questions and provide support for struggling students.
Exam Insights
Substitution techniques were cleverly tested with questions #12 and #90 on the released 2012 Practice Test. Present these questions to students only after a day or two of practice with substitution!
Student Misconceptions
Students forget to reconcile the independent variable of the integrand with their limits of integration: a student who uses the original integrand should use the original limits of integration. However, if the integrand is rewritten in terms of u, the limits of integration must be values of the function u, as well. It would be valuable to occasionally require that students rewrite the original integral in terms of u. Remind them to find new limits of integration, too.