About Course

Apply the definitive power of integration to tackle a wide range of real-world challenges. You’ll learn how to compute the exact area between curves, build and interpret accumulation functions that track total change, determine the average output of a system over time or space, and calculate volumes of complex solids by summing cross-sectional slices. Through practical examples—from land-use regions and fluid flow to material thickness and architectural forms—you’ll gain a versatile toolkit for science, engineering, economics, and beyond.

What Will You Learn?

  • Set up and compute exact areas between complex curves
  • Build accumulation functions to model total change in diverse scenarios
  • Determine average values that inform system performance and design
  • Calculate volumes of both revolution solids and slice-defined shapes
  • Translate real-world descriptions into precise integral expressions

Course Content

1. Area Between Curves
Discover how integrals let you find the region enclosed by two or more curves. You’ll learn to identify where curves intersect, choose the right slicing direction, and set up the integral that captures the exact area of any bounded shape.

  • 1.1 Identifying Bounding Curves & Intersection Points
  • 1.2 Vertical Slicing: Building the Integral from Top and Bottom Curves
  • 1.3 Horizontal Slicing & Piecewise Regions

2. Accumulation Functions
Turn a rate-of-change graph into a function that tells you how much has accumulated over time or distance. You’ll define the accumulation function, interpret its meaning in various contexts (like total distance traveled or total profit earned), and solve problems by evaluating how that total grows.

3. Average Value of a Function
Learn to compute the true average output of any process or phenomenon over a given interval. You’ll see how the average value links directly to the total accumulated area, explore examples in physics and economics, and understand why this measure matters for design and analysis.

4. Volume by Slicing
Calculate volumes of solids whose cross-sections have known shapes by integrating slice areas. You’ll practice the disk and washer methods for revolution solids, explore volumes with square, triangular, or circular cross-sections, and apply these techniques to engineering and architectural designs.

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