A utility company needs to install a cable that follows the graph of from to (both…
MATHEMATICS · Multi-part · AP · Calculus BC · Applications of Integration · Applications of Integration
Problem
A utility company needs to install a cable that follows the graph of y=f(x)=2sin(2x) from x=0 to x=6 (both measured in meters). To estimate how much cable is required, the engineers will approximate the curve’s length using Simpson’s Rule with n=6 subintervals.
(a) Write, but do not evaluate, the definite integral whose value equals the exact length of the cable.
(b) Compute the Simpson’s Rule approximation S6 for the integral in part (a). Show all work, including evaluations of the integrand at the required x-values.
(c) Using your result from part (b), estimate the percentage by which the required cable length exceeds the straight-line horizontal distance of 6 meters.