AP Calculus Mrs. Jo Brooks

Quiz 5-1

1. Explain how you find the upper and lower sum approximations when you are finding the area under a curve using rectangles.To find the upper sum approximation you use rectangles circumscribed by the curve over the interval in question and add their areas together. You do the same but with inscribed rectangles to find the lower sum approximation. The upper sum approximation will be an over estimation, the lower, an underestimation.

2. True or False. Justify your answer.If f is a positive, continuous, increasing function on [a, b], then LRAM gives an area estimate that is less than the true area under the curve.True, because the left corner of the rectangles will be on the curve, their right-hand corners will fall below the curve and thus give an under-estimate for the area.

3. An LRAM sum with 4 equal subdivisions is used to approximate the area under the sine curve from x = 0 to x = . What is the approximation?

a.

b.

c.

d.

e.

4. A truck moves with positive velocity v(t) from time t = 3 to time = 15. The area under the graph of y = v (t) between 3 and 15 gives:

a. the velocity of the truck at t = 15b. the acceleration of the truck at t = 15c. the position of the truck at t = 15d. the distance traveled by the truck from t = 3 to t = 15e. the average position of the truck in the interval from t = 3 to t = 15

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AP Calculus Mrs. Jo Brooks

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