Approximate the integral using
(a) The midpoint approximation $M_{10}$,
(b) The trapezoidal approximation $T_{10}$, and
(c) Simpson's rule approximation $S_{20}$.

Find the exact value of the integral and approximate the absolute error for each case. Express your final approximation answers to six decimal places.

$\displaystyle \int_{0}^{2} \sqrt{4x+1} \;dx=$

(a) $M_{10}=$ , $E_{M}=$ ,

(b) $T_{10}=$ , $E_{T}=$ ,

(c) $S_{20}=$ , $E_{S}=$ ,

You can earn partial credit on this problem.