How large should n be to guarantee that the approximation to 02.37cos(x2)dx\displaystyle {\int_{{0}}^{{2.37}}}{\cos{{\left({x}^{{2}}\right)}}}{\left.{d}{x}\right.} using Simpson's rule is accurate to within 0.0001? A graph of the fourth derivative of cos(x2)\displaystyle {\cos{{\left({x}^{{2}}\right)}}} follows.

n =  
Remember your answer should be an even integer.