4346 Numerical integration methods can be used in problemswhere only measured or

Chapter 7, Problem 46

(choose chapter or problem)

Numerical integration methods can be used in problems where only measured or experimentally determined values of the integrand are available. Use Simpson's rule to estimate the value of the relevant integral in these exercises.

Engineers want to construct a straight and level road \(600 ft\) long and \(75 ft\) wide by making a vertical cut through an intervening hill (see the accompanying figure). Heights of the hill above the centerline of the proposed road, as obtained at various points from a contour map of the region, are shown in the accompanying figure. To estimate the construction costs, the engineers need to know the volume of earth that must be removed. Approximate this volume, rounded to the nearest cubic foot. [Hint: First set up an integral for the cross-sectional area of the cut along the centerline of the road, then assume that the height of the hill does not vary between the centerline and edges of the road.

HORIZONTAL	HEIGHT
DISTANCE  (ft)  (ft)
	0
100	7
200	16
300	24
400	25
500	16
600	0
Figure Ex-46

Equation Transcription:

Text Transcription:

600 ft

75 ft