How to Find the Area of a Curve Using Sigma

Summation notation, or sigma, is used in mathematics to indicate the solution is a series of additions. Sigma notation is represented by the upper case Greek sigma, Σ. In calculus, sigma notation can be used to find the approximate area under a curve. It is especially useful for finding areas if you don't know the equation for the curve and therefore aren't able to calculate the area using the definite integral.

Instructions

    • 1

      Divide the curve into several horizontal segments. How many segments you divide your curve into will depend on the horizontal stretch of the curve. For example, if your curve stretches from x=0 to x=10, a practical division would be ten segments, from x=0 to x=1, x=1 to x=2, x=2 to x=3, x=3 to x=4, x=4 to x=5, x=5 to x=6, x=6 to x=7, x=7 to x=8, x=8 to x=9 and x=9 to x=10.

    • 2

      Calculate the area of a rectangle under the curve for the first division. The area is the length of the x-axis multiplied by the height of the y-axis from the x-axis to just under or just above the curve. For example, if you have divided the x-axis into segments of 1 unit each and the height of the graph at x=1 is 10, then 1 x 10 is the area of your first rectangle.

    • 3

      Calculate the area of the subsequent rectangles. In this example, calculate the area of the remaining rectangles under the curve for the segments x=1 to x=2, x=2 to x=3, x=3 to x=4, x=4 to x=5, x=5 to x=6, x=6 to x=7, x=7 to x=8, x=8 to x=9 and x=9 to x=10.

    • 4

      Add the area of all of the rectangles together to get the total area.

Tips & Warnings

  • The more divisions you make, the closer your answer will be to the actual area under the curve.
  • Shade in the rectangles you are adding up under the curve to better visualize the area.
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