Today we talked more about definite integrals and the Fundamental Theorem of Calculus
Today we continued to look at the idea of the definite integral and investigating areas underneath curves.
ONE MAJOR IDEA: If the area is above the x-axis, the area is a positive value. If the area is below the x-axis it is negative!
Be careful when combining areas on both sides
3 Khan's: Accumulation, Left and Right Riemann Sums, Midpoint and Trapezoid Sums
Today we found other ways of estimating area: trapezoid sums and midpoint sums
1 Khan: Trapezoid and Midpoint
Today we started to investigate how to write riemann sums in summation notation
Today we talked about linear approximation. Aka using a nearby known point and slope to find the approximate value of a curvy function using a straight line.
Khan: Linear Approximation
Today we introduced optimization. These questions delt with finding minimum requirements to meet certain area or volume needs.
Examples to try:
1. You are designing a cylindrical tube that must hold 1000 cm cubed of volume. If the cylindar has an open top, what is the minimum surface area required to create the cylinder?
Today we continued optimization
1 Khan Optimization