Calculus module 5 dbq

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1. The four subintervals are [0, 2], [2, 5], [5, 6], and [6, 7]. Their respective right endpoints are 2, 5, 6, and 7. If denotes the change in sea level years after 2010, then the total sea level rise over the course of 2010 to 2017 is

approximated by the Riemann sum,

2. The sum represents the definite integral

That is, we partition the interval [1, 4] into subintervals, each of width . Then we sample points in each subinterval, where is the point used in the th subinterval, then take its square root.

3. The integral is trivial:

4. Using the fundamental properties of the definite integral, we have

5. First note that is undefined at , so the integral is improper. Recall that . Then

Now,

where is any integer.