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.

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

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

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

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

$A = \pi r^2$

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

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

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

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

$A = lw$

The area between a curve and the x-axis over a specified interval.

A function that represents the antiderivative of another function, including a constant of integration (+C).

An approximation of the area under a curve by dividing it into rectangles or trapezoids.

The function being integrated.

A function whose derivative is the given function.

A function defined as the integral of another function, representing the accumulated change of that function.

A technique used to simplify integrals by substituting a function with a new variable, u.

An integral with infinite limits of integration or a discontinuity within the interval of integration.

The limit of the improper integral exists and is a real number.

The limit of the improper integral does not exist or is infinite.