Chapter 13.3, Problem 49E

Scientific Research Exercises 49 and 50 are based on the following figure, which shows the rate of publication of science research papers for researchers in the United States and the European Union in the years 1990-2010:³⁰

Here, t is time in years since 1990, and $n\left(t\right)$ is the publication rate in thousands of articles per year.

a. Use both left and right Riemann sums with five subdivisions to estimate the total number of science research papers by researchers in the United States during the 20-year period shown. [Hint: See Example 3.]

b. Use the answers from part (a) to obtain an estimate of ${\displaystyle {\int }_0^{20}n\left(t\right)}$

$dt$ for researchers in the United States.

[HINT: See Example 4.] Interpret the result.