Unit 6 Summary

Accumulating Change

I can …

  • Estimate the accumulated change of \(f(x)\) using rectangles under the curve of \(y=f(x)\) and
    • Using a left endpoint approximation (LEP)
    • Using a right endpoint approximation (REP)
  • Evaluate when a LEP or REP approximation is an under-estimate or an over-estimate.
  • Estimate the accumulated change for a table of data
  • Estimate the accumulated change of \(f(x)\) using RStudio

The Definite Integral

I can …

  • Calculate or estimate a definite integral using a sum of signed areas.
  • Interpret a definite integral of a rate of change as the total accumulated change.
  • Find the change in distance (or displacement) using a velocity versus time graph.
  • Find the change in velocity using an acceleration versus time graph.
  • Find the total cost by finding the definite integral of a marginal cost function.
  • Find the area between two curves.

The Indefinite Integral

I can …

  • Find the antiderivative(s) of our familiar functions.
  • Explain why we need “\(+ C\)” when finding antiderivatives.
  • Use the rules of integration to write a complicated indefinite integral as the sum of multiple indefinite integrals.
  • Use substitution to evaluate and integral of the form \(\int f(kx) \, dx\) where \(k\) is a constant.
  • Calculate the average value of \(f(x)\) on interval \([a,b]\) using the formula \[ \mbox{average value} = \frac{1}{b-a} \int_a^b f(x) \, dx. \]