Thread: Can someone please give a very simplified explanation of Riemann Summs

I am taking calculus 1 online and the professor doesn't answer emails especially regarding how to do something. I have done okay (average score for the class) but just don't understand it.

I know what Riemann Sums find (the area under the curve) but I am so confused on how to find it except for on the calculator. How do I know how many rectangles to break it into?

Example:
(1-x^2)dx from -1 to 1
I know the answer (according to the calculator) is 1.33 but, when I split into 2 rectangles, then it turns into 2/2 which is 1. It all comes out to 1.

I know that this is easy for most but not for me. The book does not do well at explaining things either.

Can anyone please explain this concept clearer?

Originally Posted by operaphantom2003

I am taking calculus 1 online and the professor doesn't answer emails especially regarding how to do something. I have done okay (average score for the class) but just don't understand it.

I know what Riemann Sums find (the area under the curve) but I am so confused on how to find it except for on the calculator. How do I know how many rectangles to break it into?

Example:
(1-x^2)dx from -1 to 1
I know the answer (according to the calculator) is 1.33 but, when I split into 2 rectangles, then it turns into 2/2 which is 1. It all comes out to 1.

I know that this is easy for most but not for me. The book does not do well at explaining things either.

Can anyone please explain this concept clearer?

The true area is when you take the limit of the number of rectangles going to infinity. When you approximate the area you use a finite number of rectangles and thus have an error from the true area. The more rectangles you use, the better the approximation.