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

CAL2.43 Selecting an Integration Strategy Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.43 Selecting an Integration Strategy. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.43 Selecting an Integration Strategy - Choose the most efficient technique from substitution, parts, trig identities, trig substitution, or partial fractions. 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

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Below are sample questions representative of the exercises included on this worksheet and related CAL2.43 Selecting an Integration Strategy skill assessments:

Problem 1Difficulty: Mastery
A particle has velocity \(v(t)=t e2t\) meters per second for \(0\le t\le4\). To compute the exact displacement \(\int_04 t e2t\,dt\), which strategy is most efficient?
Au-substitution
Bintegration by parts
Ctrigonometric substitution
Dpartial fractions
Solution & Explanation:Use integration by parts because t simplifies when differentiated and e2t is easy to integrate. A substitution u=2t does not eliminate the t factor; the resulting definite integral still has the product structure.
Problem 2Difficulty: Mastery
Which method is the most efficient way to evaluate \(\int \frac{x}{(x2+4)3/2}\,dx\)?
Apartial fractions
Bu-substitution
Ctrigonometric identities
Dtrigonometric substitution
Solution & Explanation:Use u-substitution with u=x2+4 because du=2x dx. The expression resembles a trig-substitution form, but the numerator supplies the inner derivative.
Problem 3Difficulty: Mastery
For \(\int \sin2(4x)\cos2(4x)\,dx\), which integration strategy is the best first choice?
Atrigonometric identities
Btrigonometric substitution
Cu-substitution
Dintegration by parts
Solution & Explanation:Use identities to rewrite sin2(4x)cos2(4x) as a multiple of sin2(8x), then apply power reduction. A direct substitution cannot remove both even powers.

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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 most efficient technique from substitution, parts, trig identities, trig substitution, or partial fractions. 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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