How to Calculate Area Under Two Curves

When you fit a number of equally sized boxes in a two-dimensional portion or shape in a plane, the sum of the boxes is what is termed as area. It is measured in unit squares, the standard unit being square meter (m^2). The question of an area under a curve can come in graph form or in equation form, each having a different approach but with the same results.

Things You'll Need

  • Calculator
  • Pen
  • Paper
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Instructions

    • 1

      Ensure your calculator can work out functions. Study the curves given, and how they intersect. Sketch them on a grid, keeping in mind the details you are putting down for future reference.

    • 2

      Calculate the equation of each curve if the question is in graph form. A straight line's formula is given as Y= Mx + C, where M is the gradient of the line while C is the point at which the line intercepts the y-axis. Note two points the line passes through and get the difference between the y-coordinates divided by the difference between the x-coordinates; the answer is the gradient. Locate the point where the straight line intercepts the y-axis, which represents C. To obtain the actual equation, replace the M with the calculated gradient and the C with the y-axis intercept point.

    • 3

      Note the functions where the two curves intersect along the x-axis. Subtract the two equations from each other and integrate the answer using your two x-functions as your boundary points. Replace the x-functions in your subtracted answer, starting with the upper limit -- which is b in the formula given -- and subtract the answer for the lower limit, which is a where a and b are the minimum and maximum function coordinates, respectively, and y2 and y1 are the equations.

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