In this video I go over another example on approximate integration and this time use the Midpoint Rule with 10 sub-intervals to approximate the integral of the function ex2 from x = 0 to x = 1. In fact there is no exact integral solution of this function and thus approximations are the only way to evaluate the integral. In this example I also go over the upper error bound for the approximation to see how accurate our approximation is with the midpoint rule.
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Approximate Integration: Example 3
a) Use the Midpoint Rule with n = 10 to approximate the integral:
b) Give an upper bound for the error involved in this approximation.
Note:
- Error estimates are upper bounds for the error.
- They give theoretical, worst-case scenarios.
- The actual error in this case turns out to be about 0.0023.