Find the exact value of $\displaystyle {\int_{{5}}^{{7}}}{x}^{{2}}{\left.{d}{x}\right.}$  .  Find the error of approximation between the exact value and the value calculated using the trapezoidal rule with four subdivisions.  Draw a graph to illustrate.

The exact value is:  Preview Question 6 Part 1 of 2  

The error in the approximation is:

Give your answer accurate to four decimal places.