Take the 2-minute tour ×  Possible Duplicate: Is my Riemann Sum
correct?  This is my second attempt, the answer seems rather odd
so I thought I would have it checked as well. For the integral:
$$\int_{-5}^{2} \left( x^{2} -4 \right) dx$$  My calculations:
$$\begin{align*}\Delta x &= \frac7n\\\\ x_i &= -5 +
\frac{7i}n\\\\ f(x_i) &= 21 - \frac{70i}{n} + \frac{49i^2}{n^2}
\\\\ A&=-738 \end{align*}$$  share|improve this question The
answer is certainly wrong. How did you get $A$? –  Arturo
Magidin May 7 '12 at 1:30 But +1 for picking up on the $\LaTeX$.
–  Brian M. Scott May 7 '12 at 1:47 add comment  marked as
duplicate by Pedro Tamaroff, Thomas, Noah Snyder, Norbert, draks
... Oct 9 '12 at 18:21   1 Answer  up vote 3 down vote accepted
The preliminary computations are fine. That means that the $n$th
right hand Riemann sum will be: $$\begin{align*} \text{RHS} &=
\sum_{i=1}^n f(x_i)\Delta x\\ &= \sum_{i=1}^n\left(21 -
\frac{70i}{n} +\frac{49i^2}{n^2}\right)\frac{7}{n}\\ &=
\frac{7(21)}{n}\sum_{i=1}^n1 - \frac{7