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

Chapter 7, Problem 44

(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.

The accompanying table gives the speeds of a bullet at various distances from the muzzle of a rifle. Use these values to approximate the number of seconds for the bullet to travel \(1800 f t\). Express your answer to the nearest hundredth of a second. [Hint: If v is the speed of the bullet and x is the distance traveled, then \(v=d x / d t\) so that \(d t / d x=1 / v\) and \(t=\int_{0}^{1800}(1 / v) d x\).]

DISTANCE  (ft)	SPEED  (ft/s)
0	3100
300	2908
600	2725
900	2549
1200	2379
1500	2216
1800	2059

Equation Transcription:

∫

Text Transcription:

1800ft

v=dx/dt

dt/dx=1/v

t=Integral^1800_0 (1/v)dx