Student Resources
Integrals: Lunar Rover
The diagram and graph below shows the velocity of a lunar rover (in miles per hour) as a function of time (in hours). The picture shows the path of the rover on the surface of the moon. The green portion of the path (terminating in a red dot) represents the approximation generated by the Left, Right, or Midpoint Sum selected with the top two sliders. Black dots mark of the segments corresponding to the terms in that sum.
Manipulate the three sliders to answer the following questions.
Use the sketch to read off the 4th term of \(L_5\). What does this number represent in the context of the lunar rover?
The applet computed the value found in the first question as a product of a velocity and a time. What is the time (in hours)?
Compare the location of the red dot in the picture of the rover’s path on the moon for \(L_{20}\) and \(R_{20}\). What can you conclude from this?
Find an error bound for \(L_{10}\) (in miles).
Compare the location of the red dot in the picture of the rover’s path on the moon for \(M_1\) through \(M_{20}\). What can you conclude from the results?
The graph of \(v\) is increasing from \(t=0\) to \(t=2\). What does this correspond to in the picture of the rover’s path on the moon?