Alvin wants to know what his average paddling rate was for a canoe trip to a campsite. On the way there it took him 7 hours agai
nst a river current of 2 km/hr. On the way back, the same distance took him 5 hours with the same 2 km/hr current. Let r= Alvin’s average paddling rate. Express the rates against the current and with the current in terms of r to complete the below table.
1 answer:
You might be interested in
Split up the integration interval into 4 subintervals:
The left and right endpoints of the -th subinterval, respectively, are
for , and the respective midpoints are
- Trapezoidal rule
We approximate the (signed) area under the curve over each subinterval by
so that
- Midpoint rule
We approximate the area for each subinterval by
so that
- Simpson's rule
We first interpolate the integrand over each subinterval by a quadratic polynomial , where
so that
It so happens that the integral of reduces nicely to the form you're probably more familiar with,
Then the integral is approximately
Compare these to the actual value of the integral, 3. I've included plots of the approximations below.
