Thread: Upper and Lower Riemann Sums

Compute the upper and lower Riemann sums and the integral from zero to 1 of f(x)dx, where the partition is

P= {0, 2/5, 1/2, 3/5, 1}

Thanks.

Originally Posted by taypez

Compute the upper and lower Riemann sums and the integral from zero to 1 of f(x)dx, where the partition is

P= {0, 2/5, 1/2, 3/5, 1}

Thanks.

What is f(x)?

f(x) = 1-x^2

Originally Posted by taypez

Compute the upper and lower Riemann sums and the integral from zero to 1 of f(x)dx, where the partition is

P= {0, 2/5, 1/2, 3/5, 1}

Thanks.

f(x) is decreasing from 0 to 1. hence, for the given partition:

Can you give me an example of a couple calculations on how you arrived at these numbers for U(f,P)? I came up with some different ones and I can't find my mistake.

Thanks.

Originally Posted by taypez

Can you give me an example of a couple calculations on how you arrived at these numbers for U(f,P)? I came up with some different ones and I can't find my mistake.

Thanks.

Because U(f,P) is calculated by taking the supremum (largest value) on each interval. So since the function was decreasing the largest value is the left-endpoint.