Final answer:
To calculate the exact area between two curves f(x) and g(x) over an interval [a,b], define the functions and interval, find the points of intersection, set up and calculate the definite integral of the absolute value of their difference. The significance of the area may vary with context, such as physical distance or economic profit.
Step-by-step explanation:
To find the exact value of the area between the graphs of y=f(x) and y=g(x) over the interval [a,b], we need clear definitions of f(x) and g(x), as well as the specified interval [a,b]. Without these specific functions and values, we can provide a general method for determining the area between two curves.
Step-by-Step Process:
Determine the points of intersection between f(x) and g(x) within the interval [a,b], if they intersect within this range.
Set up the definite integral from a to b of the absolute value of f(x) - g(x), ensuring that f(x) is the upper function and g(x) is the lower function.
Calculate the integral to obtain the area. If f(x) and g(x) switch positions between upper and lower functions within the interval, you will need to split the integral at the points of intersection.
The significance of the calculated area can relate to physical interpretations, such as the distance traveled between two points in space, or economic interpretations like the profit between cost and revenue functions over a period of time. Considering points of intersection and relevant features of the functions provides context for this area, often relating to the limits of integration and the relative positions of f(x) and g(x) on the plot.