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MATH-182 (Calculus II) Curriculum

Session 15 - Trigonometric Integrals

Handout Worksheet
Fall Semester 2026
Session Objectives & Overview

By the end of this session, you will be able to:

  • Applying Trigonometric Identities to Rewrite Integrands
  • Splitting Off Factors to Set Up uuu-Substitution
  • Utilizing Reduction Formulas for High-Power Integrals

Micro-Lecture

Engineering Context: Engineering Calculus II Application

The core mathematical skills of trigonometric integration—including splitting off specific factors, applying half-angle identities, and utilizing reduction formulas—are critical in engineering for analyzing complex periodic and wave-based phenomena. In electrical engineering, these techniques allow for the calculation of Root Mean Square (RMS) voltage and power in alternating current (AC) circuits, while in signal processing, they drive Fourier analysis to decompose communication waveforms for data compression and noise filtering. Additionally, mechanical and civil engineers use these high-power integrations to evaluate non-linear vibrations and structural resonance in systems like skyscrapers or bridges, and coastal engineers apply them to hydrodynamic wave equations to calculate energy density and ensure offshore structures can withstand severe storm surges.

Skill Block 1

Regroup 1

  • Review common misconceptions and clarify key notations.

Skill Block 2

Regroup 2

  • Reflect on the physical modeling applications and mathematical setups.

Skill Block 3

Regroup 3

  • Verify calculations and mathematical reasoning.

Synthesis Wrap-up

  • Core takeaways from Session 15 and overview of homework homework assignment.