Error Analysis In Exercises 37-40, use the error formulas to find n such that the error in the approximation of the definite integral is less than 0.0001 using (a) the Trapezoidal Rule and (b) Simpson’s Rule. See Example 3.
(a)
To calculate: The value of
Given Information:
The definite integral is
Formula used:
The simple power rule of differentiation,
The chain rule of differentiation for differential function
The quotient rule of differentiation,
The approximate value of integral
The approximate error in Trapezoidal Rule for integral
The steps to choose the value of n subdivision to calculate error:
Step:1. Find second derivative of function
Step:2. Find the maximum of
Step:3. The inequality for the error as,
Step:4
(b)
To calculate: The value of
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