Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 6 and Unit 8; FL MA.912.C.4.6, C.4.8-C.4.10; CCSS.MP2, MP3, MP5, MP6; Integrated Calculus II Standards CAL2-IMP, CAL2-NUM; TEKS 19 TAC section 111.55

CAL2.47 Convergence and Divergence of Improper Integrals Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.47 Convergence and Divergence of Improper Integrals. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.47 Convergence and Divergence of Improper Integrals - Choose whether an improper integral converges and, if so, its value. Standards tags: AP Calculus BC Unit 6 and Unit 8; FL MA.912.C.4.6, C.4.8-C.4.10; CCSS.MP2, MP3, MP5, MP6; Integrated Calculus II Standards CAL2-IMP, CAL2-NUM; 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 CAL2.47 Convergence and Divergence of Improper Integrals skill assessments:

Problem 1Difficulty: Mastery
Evaluate \(\int_0^\infty \left(\frac{1}{x+1}-\frac{2}{x+2}+\frac{1}{x+3}\right)dx\).
AConverges to \(\ln\!\left(\frac43\right)\)
BDiverges
CConverges to \(\ln 2\)
DConverges to \(0\)
Solution & Explanation:The coefficients sum to \(0\), so the logarithmic growth cancels at infinity. The antiderivative is \(\ln(x+1)-2\ln(x+2)+\ln(x+3)\); evaluating the limit gives \(-\ln(3/4)=\ln(4/3)\).
Problem 2Difficulty: Mastery
Evaluate \(\int_0^\infty \frac{x}{x2+6x+13}\,dx\).
AConverges to \(\frac{\pi}{4}\)
BConverges to \(1\)
CDiverges
DConverges to \(\ln 13\)
Solution & Explanation:For large \(x\), \(x/(x2+6x+13)\sim1/x\), so the tail is harmonic-like and diverges. An antiderivative contains \(\frac12\ln(x2+6x+13)\), which grows without bound.
Problem 3Difficulty: Mastery
Evaluate \(\int_0^\infty \frac{1}{x2+6x+13}\,dx\).
ADiverges
BConverges to \(\frac{\pi}{4}-\frac12\arctan\!\left(\frac32\right)\)
CConverges to \(\frac{\pi}{2}-\arctan 3\)
DConverges to \(\arctan\!\left(\frac32\right)\)
Solution & Explanation:Complete the square: \(x2+6x+13=(x+3)2+4\). The antiderivative is \(\frac12\arctan((x+3)/2)\), giving \(\frac{\pi}{4}-\frac12\arctan(3/2)\).

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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 and Unit 8; FL MA.912.C.4.6, C.4.8-C.4.10; CCSS.MP2, MP3, MP5, MP6; Integrated Calculus II Standards CAL2-IMP, CAL2-NUM; TEKS 19 TAC section 111.55 (Choose whether an improper integral converges and, if so, its value. Standards tags: AP Calculus BC Unit 6 and Unit 8; FL MA.912.C.4.6, C.4.8-C.4.10; CCSS.MP2, MP3, MP5, MP6; Integrated Calculus II Standards CAL2-IMP, CAL2-NUM; TEKS 19 TAC section 111.55.).

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