Chapter 8.2, Problem 56E

OTHER APPLICATION

Rate of Change of Revenue The rate of change of revenue (in dollars per calculator) from the sale of x calculators is

$R^{\prime }\left(x\right)=\left(x+1\right)\ln \left(x+1\right)$

Find the total revenue from the sale of the first 12 calculators.

(Hint: In this exercise, it simplifies matters to write an antiderivative of $x+1$ as $\frac{{\left(x+1\right)}^2}{2}$ rather than $\frac{x^2}{2}+x$.)