Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55

CAL2.26 Trigonometric Integrals with Powers of Sine and Cosine Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.26 Trigonometric Integrals with Powers of Sine and Cosine. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.26 Trigonometric Integrals with Powers of Sine and Cosine - Choose the correct identity or substitution for integrals involving powers of sine and cosine. Standards: AP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; 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 CAL2.26 Trigonometric Integrals with Powers of Sine and Cosine skill assessments:

Problem 1Difficulty: Mastery
What is ∫ from 0 to pi/2 of sin2(2x) cos3(2x) dx?
A1/15
B-1/15
C2/15
D0
Solution & Explanation:With t = 2x, the interval becomes 0 to pi and the integrand is (1/2)sin2(t)cos3(t). The odd cosine power makes the two halves cancel, so the value is 0.
Problem 2Difficulty: Mastery
What is ∫ from 0 to pi/2 of sin3(2x) cos2(2x) dx?
A1/15
B1/10
C2/15
D4/15
Solution & Explanation:Let u = cos(2x). Then du = -2 sin(2x) dx, and the bounds change from 1 to -1. The integral becomes (1/2)∫_-11(u2 - u4) du = 2/15.
Problem 3Difficulty: Mastery
What is ∫ from 0 to pi/2 of sin(x) cos9(x) dx?
A1/9
B1/10
C1/11
D1/8
Solution & Explanation:Let u = cos(x), so du = -sin(x) dx and the bounds reverse from 1 to 0. The result is ∫_01 u9 du = 1/10.

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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.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55 (Choose the correct identity or substitution for integrals involving powers of sine and cosine. Standards: AP Calculus BC Unit 6; FL MA.912.C.4.*; CCSS.MP1, MP6, MP7, MP8; Integrated Calculus II Standards CAL2-INT; TEKS 19 TAC section 111.55.).

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