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8.1 Applications to Geometry

1. Riemann sums approximate areas but not lengths and volumes.
2. The vertical slices of a cone form arches.
3. The area of a horizontal slice of the Great Pyramid of Egypt is (755/410*(410-h)^2)ft^2.
4. A curve can be divided into many little pieces, each of which is approximately straight.
5. Arc lengths as integrals are usually evaluated using antiderivatives.

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8.2 Density and Center of Mass

1. Find the quantity over a region of varying density by dividing it into many little pieces, each of which has approximately constant density.
2. The mass of a cylinder of air 25 km high can be calculated using base*height.
3. The population density of Ringsburg in Example 4 satisfies f(r) = (5-r)^2.
4. The center of mass of a mechanical system can be thought of as the balancing point for the system.
5. The center of mass of the triangle in Example 6 is calculated to be on the x-axis.

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8.3 Applications to Physics

1. Work is only done if an object moves.
2. Time has nothing to do with work.
3. The work done to slide a 5 lb book 3 feet across a floor is 15 foot-pounds.
4. What goes up must come down.
5. Water pressure is proportional to depth.