Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55

CAL2.142 Term by Term Integration Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.142 Term by Term Integration. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.142 Term-by-Term Integration - Choose the integrated power series and its interval implications. Standards: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; 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 CAL2.142 Term by Term Integration skill assessments:

Problem 1Difficulty: Mastery
Using 1/(1-t)2=Σ_{n=0}∞(n+1)tn, which series and interval represent ∫_0x 1/(1-t)2 dt?
AΣ_{n=0}∞ xn+1, interval (-1,1)
BΣ_{n=0}∞ (n+1)xn+1, interval (-1,1)
CΣ_{n=0}∞ xn+1/(n+1), interval [-1,1)
DΣ_{n=0}∞ xn, interval (-1,1)
Solution & Explanation:Integrating (n+1)tn gives xn+1. At x=1 and x=-1, terms fail to approach 0, so both endpoints are excluded.
Problem 2Difficulty: Mastery
For f(x)=Σ_{n=0}∞ (-1)n(n+1)(x/3)n, which series and interval represent ∫_0x f(t)dt?
AΣ_{n=0}∞ (-1)n xn+1/((n+1)3n), interval [-3,3]
B3Σ_{n=0}∞ (-1)n(x/3)n+1, interval [-3,3)
C3Σ_{n=0}∞ (-1)n(x/3)n+1, interval (-3,3)
DΣ_{n=0}∞ (-1)n(n+1)xn+1/3n, interval (-3,3)
Solution & Explanation:The factor n+1 cancels, giving xn+1/3n=3(x/3)n+1. At both endpoints, terms do not approach 0.
Problem 3Difficulty: Mastery
Let F'(x)=Σ_{n=0}∞ 4n(x-1)2n and F(1)=0. Which F and interval are correct?
AΣ_{n=0}∞ 4n(x-1)2n/(2n+1), interval [1/2,3/2]
BΣ_{n=0}∞ 4n(x-1)2n+1/(2n+1), interval (1/2,3/2)
CΣ_{n=0}∞ 4n(x-1)2n+1/(2n+1), interval [1/2,3/2]
DΣ_{n=0}∞ 4n(x-1)2n+1, interval (1/2,3/2]
Solution & Explanation:At x=1±1/2, the terms behave like a nonalternating odd-harmonic series in magnitude, so both endpoints diverge.

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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 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55 (Choose the integrated power series and its interval implications. Standards: AP Calculus BC Unit 10; CCSS.HSA.SSE, HSF.BF; CCSS.MP2, MP5, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-PS; TEKS 19 TAC section 111.55.).

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