Above is a graph of the miles ran by the runner and the time in minutes it has taken her to complete those miles. Drag the runner across the function F(X)= ln(1000X) to represent how many miles she has run. Then you are able to calculate the speed (Minutes per mile) of the runner by finding the derivative of the graph at that exact point.
This app will allow you to better grasp the idea of integrals by allowing you find the area under the curve of a real world function. I acquired the function from http://www.cengage.com/resource_uploads/downloads/0547167059_149912.pdf, Page 52, Problem118.
A Calculator that uses derivatives! Simple and easy way to find slope of any point in the function.
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Newton needs your help! Newton is trying to prove Kepler’s theory on planet orbits; that the area will remain constant anywhere on the orbital. Newton took the integral of the arc length to solve for the area that the planet sweeps over. The length will change in respect to the area as the area remains constant.
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