Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 6; FL MA.912.C.4.1-4.10; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-IA; TEKS 19 TAC section 111.55

CAL2.10 Antiderivatives and General Solutions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.10 Antiderivatives and General Solutions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.10 Antiderivatives and General Solutions - Select the correct general antiderivative and constant of integration for a given derivative or rate expression. Aligned with AP Calculus BC Unit 6; FL MA.912.C.4.1-4.10; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-IA; 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 CAL2.10 Antiderivatives and General Solutions skill assessments:

Problem 1Difficulty: Mastery
For x > 1, find the general antiderivative of 1/(x ln x) + 2x.
Aln(ln x) + x2 + C
B1/ln x + x2 + C
Cln x + 2 + C
D(ln x)2/2 + x2 + C
Solution & Explanation:The antiderivative of 1/(x ln x) is ln(ln x) on x > 1, and the antiderivative of 2x is x2. Add C.
Problem 2Difficulty: Mastery
A quantity R has rate R'(t) = (t + 1)/(t2 + 2t + 10) for t >= 0. Which is the general amount R(t)?
Aln(t2 + 2t + 10) + C
B(1/2) ln(t2 + 2t + 10) + C
C1/(t2 + 2t + 10) + C
Darctan(t + 1) + C
Solution & Explanation:The denominator's derivative is 2t + 2 = 2(t + 1), so the antiderivative is (1/2) ln(t2 + 2t + 10) + C. The constant represents the unknown starting amount.
Problem 3Difficulty: Mastery
Find the general antiderivative of ex cos(ex).
Asin(ex) + C
Bcos(ex) + C
Cex sin(ex) + C
D-sin(ex) + C
Solution & Explanation:Let u = ex, so du = ex dx. The integral becomes ∫ cos u du = sin u + C, giving sin(ex) + C.

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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.4.1-4.10; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-IA; TEKS 19 TAC section 111.55 (Select the correct general antiderivative and constant of integration for a given derivative or rate expression. Aligned with AP Calculus BC Unit 6; FL MA.912.C.4.1-4.10; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-IA; TEKS 19 TAC section 111.55.).

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