# help out pls

Consider the integral

∫[12,0](3x2+4x+1)dx
(a) Find the Riemann sum for this integral using left endpoints and n=4

L4=
(b) Find the Riemann sum for this same integral, using right endpoints and n=4

R4=

• I'm not sure of the definitions you use, when you write integral over the interval [12, 0] (is this intended?) does it mean the same as over the interval [0, 12], or does it mean to integrate from 12 to 0 which would imply a change of sign?

• Also, a Riemann sum depends on the chosen partition of the interval. It is not enough to know just the *number* of subintervals. Although one frequently uses equidistant partitions (x_k = a + k * (b-a)/n , k = 0,..., n), this is by no means the only choice. I guess, though, that this is what your teacher means. So you just have to add up the four numbers f(x_k) with k=0,1,2,3 (for the left endpoints) and k=1,2,3,4 for the right endpoints, and multiply by the width (12 - 0)/4 of the intervals.

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