Determine the minimum number of subintervals that should be

Question

1. Consider the integral Integral

_-1∫²(x² -4x³ -12x² + 6x -7) dx.                 (1)

Consider the use of the trapezoid method to approximate (1). Use the error estimation formula

|error| K₂(b -a)³/12n²

to determine the minimum number of subintervals that should be used to guarantee that the trapezoid method approximation of (1) is accurate to within 0.001 of the exact value of (1). Then demonstrate that this degree of accuracy is actually achieved by your approximation.

2. Repeat Exercise 1) above for Simpson's method for which the error estimation formula is |error| K₄(b-a)⁵/180n⁴