The Idea Behind Integrals

A bicyclist is biking at a rate of (12-ln(x+1)) m.p.h. where x is in hours. After biking for eight hours (he likes biking) how far has he gone?

This document requires an HTML5-compliant browser.
0 0 8

The bicyclist's velocity is shown by the graph above. The area bounded by the curve, Y=0, x=0 and x=8 gives the total distance traveled by the bicyclist after 8 hours. In order to find the area, an integral needs to be used. The integral that would model this problem is given by:

∫(12-ln(x+1) )dx evaluated from x=0 to x=8

The answer to this integral is: 84.225 miles. The bicyclist has traveled about 84.225 miles after eight hours. This total is equivalent to the area that is swept over by the red line.

App generated by Geometry Expressions