Okay please first tell me if my method is right.
I use simpsons rule, which is $$\frac{\Delta x}{3} \left[ f(x_0) + 4f(x_1) + 2f(x_2) + ... + 2f(x_{n-2}) + 4f(x_{n-1}) + f(x_n) \right]$$ where $\Delta x = \frac{b-a}{n}$
right?
So I did that and got $572.66$ for Chris, and $653.33$ for Kelly, subtracted them and got $80.67$ ft. My book is telling me the answer is $118$ ft though. What gives?
On
Just to make you feeling more comfortable with your result.
Since cBEiN already checked using both the trapezoidal and Simpson's rules, what I did was to generate interpolating functions for both sets of data and integrated the results from $t=0$ to $t=10$.
What I obtained for Kelly is $\frac{7837}{12}\approx 653.083$ and $\frac{4577}{8}=572.125 $ for Chris. So, the difference is $\frac{1943}{24}$ which is $\approx 80.958$.
So, your calculations are obviously perfectly correct and, one more, a textbook is wrong.
Someone correct me if I am wrong, but just did the calculations, and I got the same results for integrating using both the trapezoid rule and Simpson's rule, which was 570 for Chris and 651 for Kelly, so Kelly travels 81 feet further than Chris during the first 10 seconds. Your book must be wrong.