This unit's material is a collection of applications of integrals. The most important section, by far, is 6.7. In that section, we apply integrals to physical problems and start to get a sense of how useful this operation is in interpreting real-world processes.
- Section 6.6: This section gives us a method that combines the ideas of arclength and volumes of rotation. The formula ends up being more forgiving than that of arclength alone, but is still not very flexible.
- Section 6.7: The lecture here is quite short. It is little more than a reminder that the integral is a sum and that we can use this for physical problems. We have seen the idea already earlier in the chapter (in APS 162), when we discussed position as the integral of velocity and velocity as the integral of acceleration.
- Section 6.8: Here we use some hackneyed phrase like "dotting 'i's and crossing 't's." We have been using logarithms and exponentials without a proper definition of what they are when exponents are not integers. This section gives us a proper definition of the functions and can be used as practice if you suspect that your abilities with logarithms are lacking.
- Section 6.9: I cannot stress enough that this needs to be looked at as a one-topic section. The same formula that gives us the half-life of a radioactive isotope also gives us the population growth of bacteria.