Wednesday – AB. Morning (Part 1) Developing the Concept of a Definite Integral Area Model Riemann Sums and Trapezoidal Method Numerical Integration Break Morning (Part 2) Applications of Integration Solids with Known Cross Sectional Area Discovering the Average Value of a Function
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All the important concepts related to definite integrals can be taught and understood without knowing antiderivatives.
Introducing Integration through the Area Model
Figure 1 shows the velocity of an object, v(t), over a 3-minute interval. Determine the distance traveled over the interval
. The area bounded by the graph of v(t) and the t-axis for represents the distance traveled by this object. The distance can be represented by the
definite integral .
The following chart gives the velocity of a particle, v(t), at 0.5 second intervals. Estimate the distance traveled by the particle in the three seconds using three different methods. Each method is an approximation for .
Using the NUMINT program or
LMRRAM and TRAPEZOID program on a TI83/84
Create a table and a sketch for
scale for the grid is 0.5 cm
on the x and y axes
Re-sketch the graph of f (x).
The scale for this grid is 0.25 cm on
both the x and y axes.
Select one of the figures. Cut out the 9 shapes, keeping the tabs on the shape. Fold the trapezoidal trapezoidal tab. Glue the tab on the graph so that the edge of the shape is the f(x) segment. Face all the colored faces in the same direction.
Complete the Finding the Volume of the Solid Activity Sheet with your group members.
Pages 2 to 5
Pages 5 to 7
Pages 10 and 11
Pages 8 and 9
An Activity for
What Activity Would You Like to Share
Discussion of Tuesday Homework Problems
Multiple Choice Questions on the 2013 test: 3, 6, 8, 10, 11, 13, 17, 20, 21, 23, 28, 76, 78, 82, 84
2014: AB2, AB3/BC3
College Board has developed a Curriculum Module to assist you in teaching how to use Calculus to study motion.
Pflugerville High School
Motion Smartboard File
What is guaranteed?
What must be true for the guarantee?
Can parts be true if the conditions are not met?
How does it apply to real data?