Find where the graph is positive, which means above the x-axis.

Find where the slope of f(x) is positive because that would be a positive second derivative of f(x).

Look for slope changes in the graph of f(x).

Use the derivative graph, f(x), to find changes in sign of the first derivative.

Identify candidates for absolute maximum and absolute minimum for the integrally defined function.

$A = \frac{1}{2}h(b_1 + b_2)$

$\sum_{i=1}^{n} f(x_i) \Delta x$

$\sum_{i=0}^{n-1} f(x_i) \Delta x$

$\frac{\Delta x}{2} [f(x_0) + 2f(x_1) + 2f(x_2) + ... + f(x_n)]$

$A = \pi r^2$

$A = \frac{1}{2}bh$

$\frac{d}{dx} \int_{a}^{x} f(t) dt = f(x)$

$\int_{a}^{b} f(x) dx = F(b) - F(a)$

$\int u dv = uv - \int v du$

$A = lw$

Definite: has bounds, results in a number. | Indefinite: no bounds, results in a function + C.

Left: uses left endpoint for height. | Right: uses right endpoint for height. | Midpoint: uses midpoint for height.

Overestimate: Area approximation is greater than the actual area. | Underestimate: Area approximation is less than the actual area.

Relative: Local max/min within an interval. | Absolute: Overall max/min over the entire domain.

Convergent: The limit exists and is a real number. | Divergent: The limit does not exist or is infinite.