calculus riemann sum?

Question

consider the integral:
⌠7
(3 x2+2 x +5) dx
⌡1

a) Find the Riemann sum for this integral using right endpoints and n=3.
R3 =
b) Find the Riemann sum for this same integral, using left endpoints and n=3.
L3 =

Answer 1

(7-1)/3 = 2 for interval width.

R3 = 2[ f(3) + f(5) + f(7)] = 2[ 38+90+166] = 588

L3 = 2[ f(1) + f(3) + f(5)] = 2[ 10+38+90] = 276

Answer 2

Right endpoints are: 3, 5, 7
Left endpoints are: 1, 3, 5

In each case, evaluate f(x) at each of the three endpoints and multiply by the width of the interval (in this case 2). Got it?