First, here is where we were...
When I cancelled out the square from n, I forgot to carry the n through. It is below in red.
So, instead of taking out the 1/3, I just broke up the numerator and made three fractions with 3n as the denominator.
Then, I distributed the 2/n back through and simplified.
Since this is a limit at zero, everyone with an n in the denominator goes to zero.
That leaves us with adding the constants.
When we bring back in what we determined about the integral of 2 from earlier, we get...
If you remember, our estimate with the rectangles and trapezoids was 12.75. Look how close we got to the actual area, using just 4 rectangles or 4 trapezoids. I wonder how many more rectangles or triangles would shrink that 0.08333... difference?
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