Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55

CAL2.59 Area from Graphical Information Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.59 Area from Graphical Information. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.59 Area from Graphical Information - Choose the correct area expression from a labeled graph, including intersections and sign changes. Standards: AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; 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 CAL2.59 Area from Graphical Information skill assessments:

Problem 1Difficulty: Mastery

The labeled graph shows one continuous shaded region. From x=0 to x=2 the lower boundary is the x-axis and y=f(x) is above it; from x=2 to x=5 the lower boundary is y=g(x) and f remains above g. Which expression gives the total shaded area?

A∫_{0}⁵ [f(x) - g(x)] dx

B∫_{0}² [f(x) - g(x)] dx + ∫_{2}⁵ f(x) dx

C∫_{0}² g(x) dx + ∫_{2}⁵ [g(x) - f(x)] dx

D∫_{0}² f(x) dx + ∫_{2}⁵ [f(x) - g(x)] dx

Solution & Explanation:The lower boundary changes from the x-axis to g at x=2, so the area must be split. Use f-0 on the first interval and f-g on the second.

Problem 2Difficulty: Mastery

The labeled graph of y=f(x) and y=g(x) marks intersections at x=-4, -2, 1, and 3. The shaded regions are only the two lobes where f is above g: -4≤x≤-2 and 1≤x≤3. Which expression gives the total shaded area?

A∫_{-4}³ [f(x) - g(x)] dx

B∫_{-2}¹ [g(x) - f(x)] dx

C∫_{-4}^-2 [f(x) - g(x)] dx + ∫_{1}³ [f(x) - g(x)] dx

D∫_{-4}^-2 [g(x) - f(x)] dx + ∫_{1}³ [g(x) - f(x)] dx

Solution & Explanation:The graph shades only the intervals where f is above g, so integrate f minus g over those two intervals and add them. The middle lobe is not shaded in the prompt.

Problem 3Difficulty: Mastery

The labeled graph is sliced horizontally. The outer shaded region has right boundary x=R(y) and left boundary x=L(y) for -1≤y≤4, but an unshaded horizontal hole has right boundary x=B(y) and left boundary x=A(y) for 1≤y≤2. Which expression gives the shaded area?

A∫_{-1}⁴ [R(y) - L(y)] dy + ∫_{1}² [B(y) - A(y)] dy

B∫_{-1}⁴ [R(y) - L(y)] dy - ∫_{1}² [B(y) - A(y)] dy

C∫_{-1}⁴ [L(y) - R(y)] dy - ∫_{1}² [B(y) - A(y)] dy

D∫_{-1}⁴ [R(x) - L(x)] dx - ∫_{1}² [B(x) - A(x)] dx

Solution & Explanation:With horizontal slices, use right minus left in dy. The outer area is reduced by the unshaded hole, so the hole integral is subtracted.

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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 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55 (Choose the correct area expression from a labeled graph, including intersections and sign changes. Standards: AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55).