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 $$\mbox{average value} = \frac{1}{b-a} \int_a^b f(x) \, dx.$$