Find a tight upper bound for the approximation to $\displaystyle {\int_{{0.5}}^{\pi}}\frac{{\sin{{\left({x}\right)}}}}{{x}}{\left.{d}{x}\right.}$ using the midpoint rule with n = 40.
Note that the second derivative of $\displaystyle \frac{{\sin{{\left({x}\right)}}}}{{x}}$ is an increasing function on $\displaystyle {0.5}\le{x}\le\pi$.

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Include four nonzero digits in your answer.