Determine the function that defines your curve. In this example "2x + 3" is a linear function of the variable x:
f(x) = 2x + 3
Determine the endpoints, or limits, that bound the curve. Example:
Left boundary: x = 1
Right boundary: x = 5
Calculate the integral of the curve function. The method for calculating the integral varies widely depending on the type of function needed to describe the curve. Entire courses are devoted to different integration methods. Example:
integral [f(x)dx] = x^2 + 3x
Evaluate the integral at the endpoints for the curve. Example:
Left boundary: 1^2 + 3(1) = 4
Right boundary: 5^2 + 3(5) = 25 + 15 = 40
Subtract the value of the integral at the left boundary from the value of the integral at the right boundary to determine the area. Example:
Area: 40 - 4 = 36