Question

Write the Riemann sum to find the area under the graph of the function f(x) = x2 from x = 1 to x = 5.

1. the summation from i equals 1 to n of the product of the quantity squared of 1 plus 5 times i over n and 4 over n

2. the limit as n goes to infinity of the summation from i equals 1 to n of the product of the quantity squared of 1 plus 4 times i over n and 4 over n

3. the summation from i equals 1 to n of the product of the quantity squared of 4 times i over n and 4 over n

4. the limit as n goes to infinity of the summation from i equals 1 to n of the product of i over n quantity squared and 4 over n

Answer 1

well, the right-hand sum is

n
∑ f(1+i(4/n))(4/n)
i=1

there's also the left sum and the midpoint sum