The area represents the integral of the absolute difference between the two functions over a given interval.

Look for the x-coordinates (or y-coordinates if integrating with respect to y) where the curves intersect; these are the limits of integration.

The curve that is 'above' (or to the right, if integrating with respect to y) is subtracted from the curve that is 'below' (or to the left) within each interval.

Approximate the area by dividing it into rectangles or other simple shapes and summing their areas.

It indicates a value of x (or y) where the two functions have the same value, marking a potential change in which function is greater.

The area between the graph of $f(x) - g(x)$ and the x-axis represents the area between the curves $f(x)$ and $g(x)$.

Visually inspect the graph to see which function has greater y-values (or x-values if integrating with respect to y) within that interval.

If $f(x) - g(x) > 0$, then $f(x)$ is above $g(x)$; if $f(x) - g(x) < 0$, then $f(x)$ is below $g(x)$.

Look for points where the curves intersect; these points indicate where the 'top' and 'bottom' functions switch.

It shows that regardless of which function is on top, the area is always positive, as the absolute value ensures we're considering the magnitude of the difference.

$\text{Area} = \int_{a}^{b} |f(x) - g(x)| , dx$

$\text{Area} = \int_{a}^{c} (f(x) - g(x)) , dx + \int_{c}^{b} (g(x) - f(x)) , dx$

$\int x^n , dx = \frac{x^{n+1}}{n+1} + C$, where $n \neq -1$

$\text{Area} = \int_{c}^{d} |f(y) - g(y)| , dy$, where $x=f(y)$ and $x=g(y)$

$\int (ax^n + bx^m) , dx = a\frac{x^{n+1}}{n+1} + b\frac{x^{m+1}}{m+1} + C$

Set $f(x) = g(x)$ and solve for $x$.

$\int_{a}^{b} f(x) , dx = F(b) - F(a)$, where $F(x)$ is the antiderivative of $f(x)$.

$\text{Area} = \int_{a}^{b} (f(x) - g(x)) , dx$, where $f(x)$ is the top function and $g(x)$ is the bottom function.

$\text{Area} = \int_{a}^{b} |f(x) - g(x)| , dx$

$\text{Area} = \int_{c}^{d} |h(y) - k(y)| , dy$, where $h(y)$ is the right function and $k(y)$ is the left function.

A definite integral represents the area between a curve and the x-axis over a specified interval.

Points where two or more curves meet or cross each other.

The area enclosed by two or more curves within a given interval.

A method where the area is approximated by thin vertical rectangles.

Ensures that the area calculated is always positive, regardless of which curve is 'above' or 'below'.

Finding the numerical value of the definite integral, representing the area.

It defines the lower and upper bounds of the region for which the area between the curves is calculated.

The x-values where two functions, f(x) and g(x), have the same y-value, i.e., f(x) = g(x).

Finding the x-values where the y-values of both equations are the same, indicating intersection points.

The standard unit for measuring area, indicating that the area is a two-dimensional quantity.