Day 48 - Antiderivatives - 03.14.16

  • Go over Unit 3 Test
    • Average = 72%
  • Conceptual Understanding vs. Doing Problems
  • Unit 4 Test
    • Next Friday, March 25th!
  • Last Day to Remediate Unit 3 Test
    • Next Friday, March 25th!

Bell Ringer (watch the following video if you need help)

    1. What is a function f(x) in which the following is true: ?

      1. more than one answer exists

    2. Which of the following functions have a derivative of and ?

      1. none of the above

    3. Which of the following functions have a second derivative of ?

      1. more than one answer exists

      2. none of the above

    4. Solve for y:

      1. none of the above

    5. Find f(-1) based on the following:

      1. 0

      2. 1

      3. 2

      4. 3

      5. none of the above

      • Differentiation Rules
        • Power Rule
        • Constant Multiple Rule
        • Trigonometric Functions

            • How can antiderivatives be calculated using inverse differentiation rules?
            • Challenge
              • Create a reverse power rule.
                • Basically, if f'(x)=xn, what is f(x)?

              • Posted on the board at the end of the block.

              • Study!

              • APC.10
                • Use Riemann sums and the Trapezoidal Rule to approximate definite integrals of functions represented algebraically, graphically, and by a table of values and will interpret the definite integral as the accumulated rate of change of a quantity over an interval interpreted as the change of the quantity over the interval
                • Riemann sums will use left, right, and midpoint evaluation points over equal subdivisions.
              • APC.11
                • ​The student will find antiderivatives directly from derivatives of basic functions and by substitution of variables (including change of limits for definite integrals).
              • APC.12
                • ​The student will identify the properties of the definite integral. This will include additivity and linearity, the definite integral as an area, and the definite integral as a limit of a sum as well as the fundamental theorem.
              • APC.13
                • ​The student will use the Fundamental Theorem of Calculus to evaluate definite integrals, represent a particular antiderivative, and facilitate the analytical and graphical analysis of functions so defined.
              • APC.14
                • ​The student will find specific antiderivatives, using initial conditions (including applications to motion along a line). Separable differential equations will be solved and used in modeling (in particular, the equation y' = ky and exponential growth).
              • APC.15
                • ​The student will use integration techniques and appropriate integrals to model physical, biological, and economic situations. The emphasis will be on using the integral of a rate of change to give accumulated change or on using the method of setting up an approximating Riemann sum and representing its limit as a definite integral. Specific applications will include
                  • a)​ the area of a region;
                  • b)​ the volume of a solid with known cross-section;
                  • c)​ the average value of a function; and
                  • d) ​the distance traveled by a particle along a line.