MATLAB: How to find area under the curve with cumsum and cumtrapz

Question

Please help. I am trying to find the area under the curve by using cumsum and cumtrapz but I am getting the wrong answer. I think there is an issue with the syntax of the input function and I am unable to figure it out.

Best Answer

You should understand that a simple sum is not an integral. To approximate an integral using a Riemann sum, you also need to multiply by the interval. Thus, the area inside a rectangle is the product of the height and the width of the rectangle. If all you do is form the sum, you are just adding up the heights of those rectangles.

So I would predict, since the width of those rectangles is 0.01, that the cumsum would be off by a factor of roughly 100. I think that prediction comes pretty darn close.

Related Solutions

MATLAB: Difference between cumsum and cumtrapz to find area under a curve

While bearing in mind what John said, Area2 should come into much closer agreement with Area1 if cumsum is weighted by the sample spacing:

 Area2=cumsum(y)*(x(2)-x(1));

MATLAB: How to calculate the area enclosed by these 2 curves ?Image attached below….

Easy.

1. Convert the curves to cartesian coordinates, NOT polar coordinates.

2. Use polyarea.

If you tried to use polyarea on points in polar form, the result would not be correct. So you could not pass in an angle and radius, and hope that polyarea would be smart enough to know how to solve it.

Related Question

• Determining the number of divisions in riemann sums
• What is the interpretation of trapz(x,cumtrapz(x,y))

Answer 1

You should understand that a simple sum is not an integral. To approximate an integral using a Riemann sum, you also need to multiply by the interval. Thus, the area inside a rectangle is the product of the height and the width of the rectangle. If all you do is form the sum, you are just adding up the heights of those rectangles.

So I would predict, since the width of those rectangles is 0.01, that the cumsum would be off by a factor of roughly 100. I think that prediction comes pretty darn close.