Warm Up. Read the paragraph at the top of page 267 titled “Chapter 6 Overview” Then continue to read all of page 267. 6 .1 Estimating with Finite Sums. Goal: Calculate the distance traveled and use the RAM method. . Example.
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Read the paragraph at the top of page 267 titled “Chapter 6 Overview”
Then continue to read all of page 267
Since rate . time = distance:
After 4 seconds, the object has gone 12 feet.
If we draw a graph of the velocity, the distance that the object travels is equal to the area under the line.
we might guess that the
distance traveled is still equal
to the area under the curve.
We could estimate the area under the curve by drawing rectangles under the curve.
Area under the velocity curve represents the total distance traveled by an object.
Right-hand Rectangular Approximation
Left-hand Rectangular Approximation
Midpoint Rectangular Approximation
A particle moves at a velocity of
How far did the particle travel after 4 seconds.
Same Example using RRAM
Very similar to the other two.
See example #1 on page 268.
Circumscribed rectangles are all above the curve:
Inscribed rectangles are all below the curve: