If I have a table that shows x inputs: 0,3,6,9,12, and 15 and then f(x) for them: 63,62,59,52,38, and 10, how can I estimate the integral if I know it is a left Riemann sum covering the area of 0 to 15? What about if right Riemann sum?

Answer 1

since the interval width is 3, the left sum is
3(f(0)+f(3)+f(6)+f(9)+f(12)) = 3(63+62+59+52+38) = 822
the right sum is
3(f(3)+f(6)+f(9)+f(12)+f(15)) = 3(62+59+52+38+10) = 663