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Problem 5 Medium Difficulty

Use (a) the Midpoint Rule and (b) Simpson's Rule to approximate the given integral with the specified value of $ n $. (Round your answers to six decimal places.) Compare your results to the actual value to determine the error in each approximation.

$ \displaystyle \int_0^2 \frac{x}{1 + x^2}\ dx $ , $ n = 10 $

Answer

a.$M_{10} \approx 0.806598,$ error $\approx-0.001879$
b.$M_{10} \approx 0.806598, \quad$ error $\approx-0.000060$

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Video Transcript

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