HELP!!! Riemann sum

[ffuh205]

The velocity of a honey bee as it flies from the hive to a grove of flowering Ohia trees is given by the equation
v(t) =2·t·COS(t/12) + t·(t - 30)^2/(10) meters per minute. It takes 31 minutes for the bee to make the trip, time interval is [0,31].

Use a Riemann sum of 1500 pieces to approximate the integral of v(t) on the interval [0,31]. What does this represent?

Ok. I know that a Riemann sum is a right hand or left hand average or any number of methods of averaging to find the area under the curve. How in the world could I do a Riemann sum of 1500 pieces! This seems like it should be done using an applet but all the applets I’ve seen are not able to handle functions with more than one x value or more complex functions. I can't manually do it for more than n = 20 unless there is an equation I am unaware of.

 

[daon]

\(\displaystyle \Delta t = \frac{31-0}{1500} \approx 0.0206667\)

\(\displaystyle \sum_{i=0}^{1499} v(i \cdot \Delta t) \Delta t\)

Use a calculator or simple algorithm:

sum=0;
for(i=0; i < 1500; i++) sum += v(i*31/1500);
sum *= 31/1500;

 

[Deleted member 4993]

And check your answer by evaluating the integral:

\(\displaystyle \int_0^{31} v(t) dt\)

Do you know the physical interpretation of area under the v-t curve?
.