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

CAL2.12 Definite Integrals from Graphs Worksheet

Download our free printable Calculus II Math worksheet on CAL2.12 Definite Integrals from Graphs. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

Choose your preferred download format:

100% Free • No registration or login required • Instant file access

Download PDF Download DOCX

Prefer interactive practice with instant grading and explanations?Practice Definite Integrals from Graphs Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.12 Definite Integrals from Graphs. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.12 Definite Integrals from Graphs - Choose the correct signed area value from a graph using geometric regions above and below the axis. 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

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 CAL2.12 Definite Integrals from Graphs skill assessments:

Problem 1Difficulty: Mastery

For the graph of f on [0, 21], the regions between f and the x-axis are: on [0, 5], a trapezoid above the x-axis with width 5 and vertical heights 2 and 10; on [5, 11], a semicircle below the x-axis with radius 3 and diameter on the x-axis; on [11, 15], a quarter circle below the x-axis with radius 4; on [15, 17], a rectangle above the x-axis with width 2 and height 9; on [17, 21], a triangle below the x-axis with base 4 and height 6. Choose the value of ∫_{0}²¹ f(x) dx. Give an exact answer in terms of π.

A17π/2 + 60

B17π/2 - 36

C-17π/2 - 24

D-17π/2 + 36

Solution & Explanation:The signed areas are 30, -9π/2, -4π, 18, -12. Adding areas above the axis and subtracting areas below gives -17π/2 + 36 for the integral in left-to-right order. So the requested value is -17π/2 + 36. A common mistake is to add all visible areas as positive, which would give 17π/2 + 60 instead.

Problem 2Difficulty: Mastery

Use the graph of f. The bounded regions with the x-axis are: on [-2, 6], a semicircle below the x-axis with radius 4 and diameter on the x-axis; on [6, 11], a quarter circle above the x-axis with radius 5; on [11, 17], a rectangle above the x-axis with width 6 and height 5; on [17, 19], a trapezoid below the x-axis with width 2 and vertical heights 3 and 7; on [19, 22], a triangle above the x-axis with base 3 and height 4. What signed area is represented by ∫_{-2}²² f(x) dx? Give an exact answer in terms of π.

A57π/4 + 46

B7π/4 - 26

C-7π/4 + 26

D57π/4 + 26

Solution & Explanation:The signed areas are -8π, 25π/4, 30, -10, 6. Adding areas above the axis and subtracting areas below gives -7π/4 + 26 for the integral in left-to-right order. So the requested value is -7π/4 + 26. A common mistake is to add all visible areas as positive, which would give 57π/4 + 46 instead.

Problem 3Difficulty: Mastery

A coordinate-plane graph of f has these geometric regions with the x-axis from left to right: on [-5, -3], a quarter circle above the x-axis with radius 2; on [-3, 2], a rectangle below the x-axis with width 5 and height 4; on [2, 6], a trapezoid above the x-axis with width 4 and vertical heights 4 and 8; on [6, 10], a semicircle below the x-axis with radius 2 and diameter on the x-axis; on [10, 16], a triangle above the x-axis with base 6 and height 2. Find ∫_{16}^-5 f(x) dx. Pay attention to the order of the limits. Give an exact answer in terms of π.

A3π + 50

Bπ - 10

C-π + 10

D3π - 10

Solution & Explanation:The signed areas are π, -20, 24, -2π, 6. Adding areas above the axis and subtracting areas below gives -π + 10 for the integral in left-to-right order. Reversing the limits changes the sign, so the requested value is π - 10. A common mistake is to add all visible areas as positive, which would give 3π + 50 instead.

Want more practice questions with step-by-step guidance?

Practice All Questions Online

Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this CAL2.12 Definite Integrals from Graphs worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this CAL2.12 Definite Integrals from Graphs worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice CAL2.12 Definite Integrals from Graphs online with instant feedback?

Yes! In addition to this printable worksheet, students can practice CAL2.12 Definite Integrals from Graphs interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

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 (Choose the correct signed area value from a graph using geometric regions above and below the axis. 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).