Simple integration problem.

What is the cost of a swimming pool cover. the pool is bounded by $y=x^2$ and $y=2$ 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 $y=x^2$
$\int\limits_{ - \sqrt 2 }^{\sqrt 2 } {{x^2}dx}$

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

Which equals
$\frac{4\sqrt 2}{3}$ .

Area of cover is rectangle less area under the graph.
$4\sqrt{2} -\frac{4\sqrt 2}{3}$

That multiplied by 50, and then by 2
$\frac{8\sqrt 2}{3}(50)(2)$

Equals $\approx{377.123}$

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

Thanks
Regards
Craig.