How large should n be to guarantee that the Trapezoidal rule approximation to integral^8_3 (-x^4 + 22x^3 - 144x^2 + 4x + 5)dx is accurate to within 0.0001. How large should n be to guarantee that the Simpsons Rule approximation to integral^8_3 (-x^4 + 22x^3 - 144x^2 + 4x + 5)dx is accurate to within 0.0001.

Midpoint Rule: If |f"(x)| less than or equal to K for a less than or equal to x less than or equal to b then |ET| less than or equal to K(b - a)^3/12n^2

Simpson's Rule: If |f^(iv) (x)| less than or equal to K for a less than or equal to x less than or equal to b then |ES| less than or equal to K(b - a)^5/180n^4