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

definite integrals

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.