3. Use the trapezoid rule to estimate the area under the graph which represents the total energy transferred to the bat in a given time interval. Be certain to label the units of measure for total energy transferred.

Below is the usual formula for the Trapezoid Rule where h = (b - a)/n is the step size and the function f(x) is approximated over n equally spaced subintervals inside the interval [a, b]. We first input the data set.

Input := 

n = Length[thePoints] - 1
a = thePoints[[1, 1]]
b = thePoints[[n+1, 1]]
y0 = thePoints[[1, 2]]
y = Table[thePoints[[i, 2]], {i, 2, n}]
yn = thePoints[[n+1, 2]]
h = (b - a)/n

Output =

8

Output =

0

Output =

0.2

Output =

0

Output =

{0.8, 2, 3, 3, 7.5, 9, 3}

Output =

0

Output =

0.025

Input := 

TrapezoidRule =
 (h/2) (y0 + 2 Sum[y[[i]], {i, 1, n-1}] + yn)

Output =

0.7075

Accounting for units, the Total Energy is approximately 0.7075 hp seconds.