Applications of Integration

Applications of Integration

1. Area between two curves:

   • Steps to find area: 1. Graph function 2. Find intersection points 3. Shade area bounded by points 4. Draw inside rectangle representative of infinite number of rectangles in area 5. Find area of rectangle

2. Volume by known cross-sections

   • - Find the area and volume of representative shape (square, semi-circle, triangle) - Integrate it over given interval - Notice if interval indicates symmetry integrate from positive to zero instead and multi. by 2 outside integral.

3. Volume by slicing disks or washers

   • *If the disk is solid integrate where R is the distance from axis of rotation. *Revolving around x-axis:dx thick, the limits are x-values *Revolving around y-axis: dy thick, the limits are y-values *If disk has a hole, integrate the outer - inner function *For revolving around a line, include line value of line minus the value of the larger area all ^2 and smaller area all ^2.