Answer will be graded using webassign correct answer only! The speed of a runner

Question

Answer will be graded using webassign correct answer only!

The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds. ft (smaller value) ft (larger value) Estimate the area under the graph of f(x) = 10 cos(x) from x = 0 to x = pi/2. (Round the answer to four decimal places.) (a) Use four approximating rectangles and right endpoints. R4 = Is your estimate an underestimate or an overestimate? (b) Use four approximating rectangles and left endpoints. L4 = Is your estimate an underestimate or an overestimate?

Explanation / Answer

lower estimate = 0.5*[0.0 +6.7 +9.2 +14.1 +17.5 +19.4] = 33.45ft

higher estimate =0.5*[6.7 +9.2 +14.1 +17.5 +19.4 +20.2]   = 43.55ft

R4 =10* (pi/8) [cos(pi/8)+ cos(2pi/8) + cos (3pi/8) +cos(4pi/8)] = 7.90766 underestimate

L4 =10* (pi/8) [ cos (0) + cos(pi/8)+ cos(2pi/8) + cos (3pi/8)] =  11.83465 overestimate

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