Simple integration problem.

What is the cost of a swimming pool cover. the pool is bounded by $\displaystyle y=x^2$ and $\displaystyle y=2$ and it costs $2 / foot for the cover. One unit of the x and y axes are 50 feet.

I have tried the following:

Area under the graph $\displaystyle y=x^2$

$\displaystyle \int\limits_{ - \sqrt 2 }^{\sqrt 2 } {{x^2}dx}$

Which is

$\displaystyle \left. {\frac{{{x^3}}}{3}} \right|_{ - \sqrt 2 }^{\sqrt 2 }$

Which equals

$\displaystyle \frac{4\sqrt 2}{3}$.

Area of cover is rectangle less area under the graph.

$\displaystyle 4\sqrt{2} -\frac{4\sqrt 2}{3}$

That multiplied by 50, and then by 2

$\displaystyle \frac{8\sqrt 2}{3}(50)(2)$

Equals $\displaystyle \approx{377.123}$

My textbook has $18,856. I am not even in the same ball park.

Thanks

Regards

Craig.