Applications of Integration

Applications of Integration

1. Area Between Two Curves

   • Steps in finding area:
     • 1. Sketch the equations.
       • 2. Find the intersection points of the two equations.
       • 3. Shade the area bounded by the two equations.
       • 4. Draw a rectangle representative of the infinite number of rectangles in the area.
       • 5. Find the area of the rectangle.
       • 6. Sum the infinite number of rectangles using one of the integration formulas to find the area of the region.

2. Volume by Disk and Washer

   • Equations solved for y (Vertical) = π ∫ydx
   • Equations solved for x (Horizontal) = π ∫xdy
   • Equation for a disk with a hole in it: v(outer) - v(inner)
   • Use the area found in the area between two curves

3. Solids With Known Cross Sections

   • Steps to finding solids with known cross sections:
     • 1. Find the area and volume of the representative shape (Square, semi-circle, triangle, etc)
       • 2. Integrate it over the given interval to sum an infinite number of the shape.