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Approximate the integral using (a) the midpoint approximation $M_{10},$ (b) the trapezoidal approximation $T_{10},$ and $(c)$ Simpson's rule approximation $S_{...

Question

Approximate the integral using (a) the midpoint approximation $M_{10},$ (b) the trapezoidal approximation $T_{10},$ and $(c)$ Simpson's rule approximation $S_{20}$ using Formula (7). In each case, find the exact value of the integral and approximate the absolute error. Express your answers to at least four decimal places. $\int_{4}^{9} \frac{1}{\sqrt{x}} d x$

Approximate the integral using (a) the midpoint approximation $M_{10},$ (b) the trapezoidal approximation $T_{10},$ and $(c)$ Simpson's rule approximation $S_{20}$ using Formula (7). In each case, find the exact value of the integral and approximate the absolute error. Express your answers to at least four decimal places. $\int_{4}^{9} \frac{1}{\sqrt{x}} d x$



Answers

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 $


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