Applications of integral: area between a curve and the x- axis

Objective: Find the area between the curve of a function f and the x-axis over an interval [a b].

Definition

The area between the curve of a function and the x-axis bounded by the verticals x = a and x = b is given by

The area is positive if it is located above the x-axis and negative if it is below.



The areas A(2), A(4) are negative. The areas A(1), A(3) and A(5) are positive. The total area is the sum of all the areas: positive and negative.

Example 



Solution

Practice

  

 

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