Understanding Signed Area Between Curves and Their Intersection Points

DESCRIPTION

This content explores the concept of signed area in the context of functions where the graph of y = f(x) falls below the x-axis between specific points a and b, indicating a negative value for the area. It includes examples to illustrate how to find the finite area enclosed between two graphs. Additionally, it covers the process of determining the points of intersection for two curves and calculates the area trapped between the graph of a function and the x-axis, specifically for x > 0.

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May 15, 2026

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Understanding Signed Area Between Curves and Their Intersection Points

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y a b x When the portion of the graph of y = f(x) is below the x-axis between x = a and x = b then the value of will be negative. Area
Area Entrapped between two curves
Example Find the finite area enclosed between the graph of and
Example • Find the points of intersection for the graphs of and • Hence find the finite area enclosed between the graph of and
y 0 x Example • The graph drawn above is of the line and the curve • Find the points of intersection for the graphs and • Hence find the finite area enclosed between the graph of and • for x > 0.