Final answer:
The Midpoint Rule is a method for approximating the definite integral, and the error can be approximated using a formula involving the second derivative of the function.
Step-by-step explanation:
Rule for approximating the definite integral with the Midpoint Rule:
The Midpoint Rule is a method for approximating the definite integral of a function. It involves dividing the interval [a, b] into subintervals of equal width, calculating the value of the function at the midpoint of each subinterval, and then multiplying this value by the width of the subinterval. Finally, the individual subinterval approximations are added together to obtain the approximate value of the definite integral.
Approximating the error for the Midpoint Rule:
The error for the Midpoint Rule can be approximated using the formula:
Error = (b - a)(k * (f''(c))),
where (f''(c)) is the second derivative of the function evaluated at some point c in the interval [a, b], and k is a constant that depends on the number of subintervals used.