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

CAL2.14 Properties of Definite 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 CAL2.14 Properties of Definite Integrals. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.14 Properties of Definite Integrals - Select the correct simplification using additivity, reversal of bounds, constant multiples, or comparison properties. Standards: AP Calculus BC Unit 6; FL MA

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 CAL2.14 Properties of Definite Integrals skill assessments:

Problem 1Difficulty: Mastery
Let a < b < c, b-a = 2, c-b = 5, ∫_ab f(x) dx = -3, and ∫_bc f(x) dx = 4. What is ∫_ca (2f(x)-3) dx + ∫_ba (f(x)+1) dx?
A-20
B18
C-18
D20
Solution & Explanation:Since ∫_ac f=-3+4=1, ∫_ca f=-1 and ∫_ca 1=a-c=-7, so ∫_ca(2f-3)=2(-1)-3(-7)=19. Also ∫_ba(f+1)=3-2=1. The total is 20.
Problem 2Difficulty: Mastery
If a < b and f(x) ≤ g(x) on [a,b], which statement is guaranteed for the reversed integrals?
A∫_ba f(x) dx ≤ ∫_ba g(x) dx
B∫_ba f(x) dx = ∫_ba g(x) dx
C∫_ba f(x) dx ≥ ∫_ba g(x) dx
D∫_ab f(x) dx ≥ ∫_ab g(x) dx
Solution & Explanation:On [a,b], comparison gives ∫_ab f≤∫_ab g. Reversing both integrals multiplies both sides by -1, so the inequality reverses.
Problem 3Difficulty: Mastery
If ∫_ab f(x) dx = 6 and ∫_ba g(x) dx = -2, what is ∫_ab (4f(x)-3g(x)) dx + ∫_ba (f(x)+g(x)) dx?
A26
B10
C-10
D-26
Solution & Explanation:The reversed information gives ∫_ab g=2. The first integral is 4(6)-3(2)=18. The second is -∫_ab(f+g)=-(6+2)=-8. The sum is 10.

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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 simplification using additivity, reversal of bounds, constant multiples, or comparison properties. Standards: 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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