Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the given integral with the specified value of n.
(Round your answers to six decimal places.)
\int_0^1 \sqrt{3x}e^{-x^2} dx, \quad n = 10
(a) the trapezoidal rule
(b) the midpoint rule
(c) Simpson's rule
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Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the given integral with the specified value of n.
(Round your answers to six decimal places.)
\int_1^5 \frac{\cos(4x)}{x} dx, \quad n = 8
(a) the trapezoidal rule
(b) the midpoint rule
(c) Simpson's rule