$A = \int_{a}^{b} [f(x) - g(x)] dx$, where $f(x) \ge g(x)$ on $[a, b]$.

$A = \int_{0}^{2} (e^x - x) dx$

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

$\int e^x dx = e^x + C$

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

$A = \int_{-2}^{B} [ln(x+3) - (x^4 + 2x^3)] dx$

$A = \int_{a}^{b} (top \ function - bottom \ function) dx$

$\int_{a}^{c} (f(x) - g(x)) dx + \int_{c}^{b} (g(x) - f(x)) dx$, where c is the intersection point.

$\int x^n dx = \frac{x^{n+1}}{n+1} + C$

$\int [f(x) \pm g(x)] dx = \int f(x) dx \pm \int g(x) dx$

1. Find intersection points. 2. Determine top/bottom functions. 3. Set up the integral: $\int_{a}^{b} (top - bottom) dx$. 4. Evaluate the integral.

1. Set $f(x) = g(x)$. 2. Solve for x. 3. Use a calculator if needed.

1. Graph the functions. 2. Choose a test point within the interval. 3. Evaluate both functions at the test point; the larger value is the 'top' function.

1. Identify the limits of integration (a and b). 2. Write the integrand as (top function - bottom function). 3. Include 'dx'.

1. Find the antiderivative of the integrand. 2. Evaluate the antiderivative at the upper and lower limits. 3. Subtract: F(b) - F(a).

1. Find all intersection points. 2. Split the integral into multiple integrals at each intersection. 3. Determine the top/bottom function for each interval. 4. Sum the absolute values of each integral.

1. Graph the functions and visually estimate the area. 2. Compare your calculated area with the estimate. 3. Use a calculator to verify the definite integral.

Use a calculator with numerical integration capabilities to approximate the definite integral.

1. Find intersection points using calculator. 2. Set up integral. 3. Evaluate integral using calculator.

1. Find intersection points. 2. Determine which function is on top. 3. Integrate the difference between the functions.

The area enclosed by two or more functions, found by integrating the difference between the functions over a given interval.

A definite integral calculates the area under a curve between two specified limits (bounds) on the x-axis.

The function with greater y-values over a given interval, used as the minuend in the integral.

The function with lesser y-values over a given interval, used as the subtrahend in the integral.

The x-values where the curves intersect, defining the interval over which the area is calculated.

Points where the graphs of two functions have the same x and y values.

A tool to find intersection points and visualize which function is 'on top'.

The area bounded by the intersection of two or more curves.

The function that is being integrated.

To find the numerical value of the definite integral, representing the area.