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

CAL2.57 Area Between Curves with Respect to y Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.57 Area Between Curves with Respect to y. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.57 Area Between Curves with Respect to y - Choose the correct integral setup when horizontal slices create a simpler area expression. 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

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Below are sample questions representative of the exercises included on this worksheet and related CAL2.57 Area Between Curves with Respect to y skill assessments:

Problem 1Difficulty: Mastery
R is the right half of the disk \(x2+(y-1)2\le 9\), bounded on the left by the y-axis. Which dy-integral gives its area?
A\(\int_{-3}3[(\sqrt{9-y2})-(0)]\,dy\)
B\(\int_{-2}4[(0)-(\sqrt{9-(y-1)2})]\,dy\)
C\(\int_{-2}4[(\sqrt{9-(x-1)2})-(0)]\,dx\)
D\(\int_{-2}4[(\sqrt{9-(y-1)2})-(0)]\,dy\)
Solution & Explanation:The circle is centered at (0,1) with radius 3, so y runs from -2 to 4. On the right half, x=sqrt(9-(y-1)2), and the y-axis is x=0.
Problem 2Difficulty: Mastery
For \(0\le y\le 1\), the region R lies between \(x=y2\) and \(x=\sqrt{y}\). Which integral gives the area of R using horizontal slices?
A\(\int_{0}1[(y2)-(\sqrt{y})]\,dy\)
B\(\int_{-1}1[(\sqrt{y})-(y2)]\,dy\)
C\(\int_{0}1[(\sqrt{y})-(y2)]\,dy\)
D\(\int_{0}1[(\sqrt{x})-(x2)]\,dx\)
Solution & Explanation:On 0 <= y <= 1, sqrt(y) is greater than y2, so it is the right boundary. The setup must use dy because the slice height is y.
Problem 3Difficulty: Mastery
The region R is enclosed by \(x=1-(y-1)2\) and the y-axis. Which dy-integral gives the area?
A\(\int_{-1}1[(1-y2)-(0)]\,dy\)
B\(\int_{0}2[(1-(y-1)2)-(0)]\,dy\)
C\(\int_{0}2[(0)-(1-(y-1)2)]\,dy\)
D\(\int_{0}1[(1-(y-1)2)-(0)]\,dy\)
Solution & Explanation:The curve meets the y-axis at y=0 and y=2, and it lies to the right of the y-axis between those values.

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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 integral setup when horizontal slices create a simpler area expression. 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.).

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