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Area under a Curve

The area between the graph of y = f(x) and the x-axis is given by the definite integral below. This formula gives a positive result for a graph above the x-axis, and a negative result for a graph below the x-axis.

Note: If the graph of y = f(x) is partly above and partly below the x-axis, the formula given below generates the net area. That is, the area above the axis minus the area below the axis.

Formula:

  
Example 1:

Find the area between y = 7 – x2 and the x-axis between the values x = –1 and x = 2.


Example 2:

Find the net area between y = sin x and the x-axis between the values x = 0 and x = 2π.


See also

Area between curves, area using parametric equations, area using polar coordinates

 


  this page updated 27-aug-12
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes