Question

The following table gives the approximate amount of emissions, E, of nitrogen oxides in millions of metric tons per year in the US. Let t be the number of years since 1940 and E=f(t).
1940 1950 1960 1970 1980 1990
t 0 10 20 30 40 50
E 6.8 9.2 13.4 18.1 20.8 19.2
Estimate the integral: ∫^50_0f(t)dt≈

Answer 1

Using the trapezoidal rule, we can estimate the integral as:

∫^50_0f(t)dt ≈ (10/2)(6.8 + 9.2) + (10/2)(9.2 + 13.4) + (10/2)(13.4 + 18.1) + (10/2)(18.1 + 20.8) + (10/2)(20.8 + 19.2)

Simplifying and computing, we get:

∫^50_0f(t)dt ≈ 940 million metric tons

Therefore, an estimate for the integral is 940 million metric tons.