area between a continuous function and x-axis. trip from cc-san antonio make a narrative for the...
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Units of Line and Area Rise/run = miles/hour
Fill region with rectangles
Units of area = length*width = hours*miles
• What is the average velocity (rate of change of distance)?
• What is the average distance from CC during the traveled time?
• What degree polynomial would you use to fit this graph?
Area vs. Absolute AreaArea of a rectangle = length*width or base*height
Base 5, height 1Area = 5Absolute Area =5
Base 5, height -2Area = -10Absolute area= 10
An Example to Understand the Techniques
AREA BETWEEN A STRAIGHT LINE AND THE X-AXIS ON A CLOSED INTERVAL
Grid (Boxes)
Make a grid. Estimate the number of rectangles needed to fill up the region Estimate area of one rectangleArea No Boxes*Area one box≅
Indivisibles
Indivisible at each end point Average of all Indivisibles
The area of the rectangle obtained above is approximated by calculating the Average value of the heights at the end
points and multiply the average by the length of the interval.
The area between the graph of the continuous function y=f(x)and the x-axis on the interval [a ,b] is denoted
Exercise 2
i) Find an overestimate and underestimate for the ii) Estimate the area using seven subdivisions
a. Grid technique. b. Left-hand rectangles. c. Indivisibles.
For questions (ii) (a-c), also write the expression using summation notation.
Exercise 3
i) Find and overestimate and lower estimate for the area. ii) Estimate the area using rectangles and twelve subdivisions (use summation notation and the calculator).
Find the area of the region and use it to determine the average distance between the car and CC for the
whole length of the trip.