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

## 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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