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

Answer:

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

Step-by-step 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