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***SOLVED*Riemann Sum Question**

*SOLVED*

My question is quite simple. I probably just missed something somewhere. I've looked for hours and cannot find the mistake.

## Homework Statement

Find the area under the curve using the definition of an integral and Gauss summation equations:

f(x) = 3 - (1/2)x

where x is greater than or equal to two and less than or equal to 14

## Homework Equations

Formula #1: Gauss equation for the sum of a list simple list of numbers eg 1,2,3,etc.:

[n(n+1)]/2

Formula #2: to find area using Riemann sums:

lim as n→∞ of Ʃ from i=1 to n of:

f[(i*(b-a))/n]*[(b-a)/n]

## The Attempt at a Solution

Using Formula #2:

lim as n→∞ of Ʃ from i=1 to n of:

f[12i/n]*(12/n)

pulling out 12/n from under the summation sign:

lim as n→∞ of 12/n * Ʃ from i=1 to n of:

3 - (6i/n)

pulling 36/n out from underneath the summation sign because it has no "counting" i variable:

lim as n→∞ of 36/n - (72/n^2) * Ʃ from 1 to n of i

Using Formula #1 to get rid of the summation sign:

lim as n→∞ of 36/n - (72n^2 + 72n)/2n^2

crossing out the factors n^2 and 2, which are in the N and D of the 2nd fraction:

lim as n→∞ of 36/n - 36 - 36/n

taking the limit:

-36

**Now what's the problem?**

∫

^{14}

_{2}3 - (1/2)x dx = -12

What went wrong? Again, I've been checking this thing for hours.

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