Using Simpson’s Rule

Approximate the following integrals using Simpson’s Rule Experiment with values of n to ensure that the error is less than 10−3.

Problem 44E

Using Simpson’s Rule

Approximate the following integrals using Simpson’s Rule Experiment with values of n to ensure that the error is less than .

Solution:Step 1</p>

The error for the approximation for Simpson’s Rule is

Step 2We calculate , by finding the derivative of

Through the graph given below the maximum value of the is 10.8477.

Step 3Using the value in the error formula, we getSince error is less that 10-3, putting the values of we getSolving this for n, we get

Step 4Now, we have the value of n, such that the error is less than 10-3.Using this we approximate the function.

Hence, the approximate value of the function is 0.4907.