⚠️ DRAFT HANDOUT - NOT FINALIZED BY INSTRUCTOR - DO NOT PRINT YET

MATH-182 (Calculus II) Curriculum

Session 02 - Area Under the Curve

Handout Worksheet
Fall Semester 2026
Session Objectives & Overview

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

  • Analytical Evaluation via FTOC & Integration Techniques
  • Fluency with the Properties of Definite Integrals
  • Geometric Interpretation & Understanding Net Signed Area

Micro-Lecture

Engineering Context: Engineering Calculus II Application

In engineering, calculating the area under a curve is fundamental to translating continuous physical data into system logic, such as accumulating instantaneous acceleration over time to determine a vehicle's exact velocity and position. Whether mechanical engineers are integrating variable forces to compute total rocket payload work, civil engineers analyzing bridge load distributions to pinpoint structural stress, or electrical engineers utilizing integral properties to evaluate alternating current (AC) signal power without opposing waves canceling out, these three calculus skills underpin modern simulation software. By combining geometric spatial awareness, algebraic interval manipulation, and analytical evaluation, engineers successfully transform fluctuating real-world rates of change into stable, predictable designs.

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 02 and overview of homework homework assignment.