Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55

CAL2.22 Choosing u and dv Strategically Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.22 Choosing u and dv Strategically. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.22 Choosing u and dv Strategically - Choose the best u and dv choices for integration by parts using structure, differentiation, and simplification. Standards: AP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Calculus II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related CAL2.22 Choosing u and dv Strategically skill assessments:

Problem 1Difficulty: Mastery
For ∫ x4 arctan(x5) dx, which setup best creates a substitution-friendly follow-up integral after one step?
Au = x4, dv = arctan(x5) dx
Bu = arctan(x5), dv = x4 dx
Cu = x4 arctan(x5), dv = dx
Du = 1, dv = x4 arctan(x5) dx
Solution & Explanation:Choose u = arctan(x5) and dv = x4 dx. Then du = 5x4/(1 + x10) dx and v = x5/5, so the remaining integral has the matching x9 dx structure for a substitution.
Problem 2Difficulty: Mastery
For ∫ x3 arctan(x2) dx, which setup best leaves a rational integral after differentiating u?
Au = x3, dv = arctan(x2) dx
Bu = x3 arctan(x2), dv = dx
Cu = arctan(x2), dv = x3 dx
Du = 1, dv = x3 arctan(x2) dx
Solution & Explanation:Choose u = arctan(x2), since du = 2x/(1 + x4) dx, and choose dv = x3 dx. The resulting integral is rational after combining powers, while putting arctan(x2) in dv is much less direct.
Problem 3Difficulty: Mastery
For ∫ x3/(1 + x2)^(3/2) dx, which setup is most strategic?
Au = (1 + x2)^(-3/2), dv = x3 dx
Bu = x3, dv = (1 + x2)^(-3/2) dx
Cu = 1, dv = x3/(1 + x2)^(3/2) dx
Du = x2, dv = x(1 + x2)^(-3/2) dx
Solution & Explanation:Split x3 as x2·x. Then dv = x(1 + x2)^(-3/2) dx integrates by substitution, and u = x2 differentiates to a simpler factor.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Calculus II Math students. It aligns with educational standard AP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55 (Choose the best u and dv choices for integration by parts using structure, differentiation, and simplification. Standards: AP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55.).

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