Question

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.

x3 sin(x) dx, n = 8
1) The Trapezoidal Rule
2) The Midpoint Rule
3) Simpson's Rule

Answer 1

1. -1392.09
2. -1744.43
3. -1636.41

Explanation:

using the given integral

calculate: Δx = (12-0) / 8 = 3/2

Xo = 0, f(x) =
`x^3sin(x)`

X1 = 3/2 , X2 = 3, X3 = 9/2, X4 = 6, X5 = 15/2, X6 = 9, X7 = 21/2, X8 = 12

Inputting the given values into the Trapezoid rule, midpoint rule and Simpson's rule to approximate the given integral with the specified value of n = 8