```{r echo=FALSE,results="hide",label="options",echo=FALSE}
require(knitr, quietly=TRUE)
opts_chunk$set(fig.width=3,fig.height=3,out.width="3in")
```
```{r warning=FALSE,error=FALSE,message=FALSE,results="hide",echo=FALSE}
library(mosaic,quietly=TRUE)
trellis.par.set(theme=col.mosaic())
```
Integration Modeling Settings
-----------------
### Net present value of dividend streams.
Discount future dividends at a rate that decreases to zero to account for the subjective belief that the company will be obsolete in 10 years.
### Models of car distance
How much difference does the precise model of velocity versus time make?
### Fun on the slide.
Integrate up the instantaneous fun.
### Monte Carlo integration
How close is the Monte Carlo method to the actual integral? How would you know how close you are?
### Popcorn versus time.
From a sound recording of popcorn (to be made), sketch qualitatively and subjectively the rate of popping against time. Integrate this to get the total subjective amount, then normalize to the actual amount, then differentiate to get the actual rate of popping.
## Exercises
1. Using ```D()``` to answer questions about integrals. [Rmd](../Topics/Integration/Integration-problem201.Rmd)
2. The potential energy of the stone in the Great Pyramid of Giza. Find the density of sandstone and the volume of each layer in the pyramid. Assuming that the workers can deliver the energy at a constant rate, how tall would the pyramid grow as a function of time?