# Math BM

Quarter Three Benchmark

Approximating/Finding Areas Under Curves

By Nathan Kamal and Rick Kinard

Hello! Welcome to our calculus benchmark. This qfjgoogroduction to integrals, and methods to approximate the area under a curve. The assignment was to select a set of data from any real-world situation with an independent and dependent variable, the dependent variable being a rate. We chose acceleration, the relationship between velocity and time, using a set of data collected from a 2010 Artega GT. Below is a v/t chart and graph.

 V mph 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 T sec 1.3 1.7 2 2.4 3 3.5 4 4.8 5.5 6.3 7.2 8.3 11 14 18 Now that we can visualize our data in the form of a graph, we can find the area under the curve over a given interval to calculate distance. Because a distance/time function is the derivative function of velocity/time function, we can use integrals to find how far the car has travelled, by using a t/v graph (in this case, the graph is actually TIME as a function of VELOCITY, due to the fact that time is a fixed, independent variable). We can approximate the area by using trapezoids and rectangles.   