Question

If I have y=e^x and know it represents the left Riemann sum with n=2 approximating ∫ with upper limit of 1 and lower limit of 0 e^x dx. How do I write out the terms of the sum without evaluating it? Similarly, how would I do that with the right Riemann sum?

Answer 1

clearly you need to review Riemann sums. This would be
left sum = 1/2 (f(0) + f(1/2))
right sum = 1/2 (f(1/2) + f(1))

Answer 2

Right, but I have to only put down two things that get added together. I do not understand how to include the 1/2. Without the 1/2, wouldn't it be 1+e^(1/2) for the left and then e^(1/2)+e for the right? But then how can I show the 1/2 when only able to show two things being added?

Answer 3

Really? If you only want the sum, then just distribute the 1/2 over each term

e(0)/2 + e(1/2)/2
e(1/2)/2 + e/2