Suppose the Trapezoidal Rule is used with n = 4 to approximate the value of ∫2−2(3x2−2x+1)dx . What is the error, ET ?
To calculate the error, ET, for the Trapezoidal Rule with n = 4, we need to use the formula for the error bound:
ET = -(b-a)3f''(c) / 12n^2
Given that the function is f(x) = 3x^2 - 2x + 1 and the interval is from -2 to 2, we can find the second derivative of the function:
f'(x) = 6x - 2
f''(x) = 6
Now we can plug in the values into the error bound formula:
ET = -(-2-2)3(6) / (12*4^2)
ET = -4 * 18 / (12 * 16)
ET = -72 / 192
ET = -3 / 8
ET = -0.375
Therefore, the error, ET, for the Trapezoidal Rule with n = 4 is -0.375.