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Considering the function $$f(x)=\frac{x+1}{x+2} $$
and given that $f(x)$ is a decreasing function on [0, 3], how do I determine a lower sum estimate for the area between the curve $y = f(x)$ and the $x$-axis on the interval [0, 3] with 3 equal subdivisions?
Use the definition of Lower Sum. Have you been given a partition? The simplest partition is $P=\{0,3\}$ and wrt to this, the estimate would e $3*f(3)$, since $f(3)$ is the minimum value taken by $f$ on the interval (using the information given about $g$ being decreasing).
HINT. You want $3$ equal subdivisions, so clearly you divide $[0,3]$ into $0-1$, $1-2$, $2-3$. Now $f(x)$ is decreasing. So is it biggest at the left end of an interval, the right end, or somewhere in the middle? What values do you then use for $f(x)$ in your sum?
