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.

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

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

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

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

$A = \pi r^2$

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

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

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

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

$A = lw$

The derivative of the integral of a function is the original function itself.

The definite integral of a function can be evaluated by finding the difference of its antiderivative at the upper and lower limits of integration.