Chapter 6, Problem 13TYS

(a)

To determine

To calculate: The value of $n$ such that the error in the approximation of the definite integral ${\displaystyle \underset{0}{\overset{1}{\int }}\left(2x^6+1\right)dx}$ is less than 0.01 by using the error formula in the Trapezoidal Rule.

(b)

To determine

To calculate: The value of $n$ such that the error in the approximation of the definite integral ${\displaystyle \underset{0}{\overset{1}{\int }}\left(2x^6+1\right)dx}$ is less than 0.01 by using the error formula in the Simpson’s Rule.