current attempt in progress explain in words what the integral represents and give units. ∫19862002f(t)dt…
current attempt in progress explain in words what the integral represents and give units. ∫19862002f(t)dt, where f(t) is the rate at which the worlds population is growing in year t, in billions of people per year. the integral represents the the units are etextbook and media save for later attempts: 0
Answer
Explanation:
Step1: Recall integral meaning
The definite - integral $\int_{a}^{b}f(t)dt$ of a rate - function $f(t)$ over an interval $[a,b]$ gives the net change of the quantity that $f(t)$ is the rate of. Here, $f(t)$ is the rate of population growth.
Step2: Determine integral representation
The integral $\int_{1986}^{2002}f(t)dt$ represents the net change in the world's population from the year 1986 to 2002.
Step3: Find the units
The units of $f(t)$ are billions of people per year, and the units of $dt$ are years. When we multiply the units of $f(t)$ and $dt$ and integrate, the units of $\int_{1986}^{2002}f(t)dt$ are billions of people.
Answer:
The integral represents the net change in the world's population from 1986 to 2002. The units are billions of people.