The problem

Use Definition 2 to find an expression for the area under the graph of f as a limit. do not evaluate the limit.

Definition 2 is

$\displaystyle A = \lim_{n->\infty} R_{n}= \lim_{n->\infty} [f(x_{1})\Delta x+f(x_{2})\Delta x+....+f(x_{n})\Delta x]$

17. $\displaystyle f(x)=\sqrt[4]{x}, 1 \leq x \leq 16 $

I got

$\displaystyle \lim_{n->\infty} \sum^n_{i=1} [f(x_{i}) \times

\frac{b-a}{n}]

$

$\displaystyle =\lim_{n->\infty} \sum^n_{i=1} [f(x_{i} \times \frac{15}{n}]$

$\displaystyle =\lim_{n->\infty} \sum^n_{i=1} [f(\frac{15i}{n})\times\frac{15}{n}]$

$\displaystyle =\lim_{n->\infty} \sum^n_{i=1} [\sqrt[4]{\frac{15i}{n}}\times \frac{15}{n}]$

but the book's answer is

$\displaystyle \lim_{n->\infty} \sum^n_{i=1} [\sqrt[4]{1 + \frac{15i}{n}}\times \frac{15}{n}]$

where did that extra 1 come from?