Mississippi Math C.A.21

MathGrades 9–12Algebra (A) Demonstrate Basic Knowledge of Functions, Including their Behavior and Characteristics

The Standard

Apply the power rule and u-substitution to evaluate indefinite integrals.

2025 Mississippi College- and Career-Readiness Standards for Mathematics · Employ Various Integration Properties and Techniques to Elevate Integrals

Teacher's field guide

What Students Need to Do: Students find antiderivatives of powers of x. For expressions such as 2x(x²+1)², they set u=x²+1 and replace 2x dx with du. They return to x and add C.
What Mastery Looks Like: A student finds ∫x⁴ dx = x⁵/5+C and ∫2x(x²+1)² dx = (x²+1)³/3+C. They check each answer by differentiating.
Common Misconceptions: Some students multiply by the new exponent instead of dividing. Others replace x²+1 with u but leave 2x dx unchanged, forget to return to x, or drop C.
How to Assess It: Exit ticket: Evaluate ∫[x⁴+2x(x²+1)²] dx. Show the substitution for the second term, then check your answer by differentiating.

Lesson moves

Give pairs cards for 2x(x²+1)² dx, u=x²+1, and u² du; have them arrange the cards and solve.
Ask students to write why ∫2x(x²+1)² dx calls for substitution but ∫x⁵ dx does not.
Run a three-minute matching game with cards showing integrals and antiderivatives; students confirm each match by differentiating.
Give a tank rate of 2t(t²+1)² liters per minute and a starting volume of 5 liters; have students find the volume function.

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