Use the trapezoidal rule with $n = 5$ to approximate
$\int_{1}^{6} \frac{\cos (x)}{x} d x$

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Substitute these values into the trapezoidal rule formula: $\int_{1}^{6} \frac{\cos (x)}{x} d x \approx \frac{1}{2} [\frac{\cos (1)}{1} + 2 * \frac{\cos (2)}{2} + 2 * \frac{\cos (3)}{3} + 2 * \frac{\cos (4)}{4} + 2 * \frac{\cos (5)}{5} + \frac{\cos (6)}{6}]$

Steps

Step 1 ：Calculate the width of each subinterval: $h = \frac{b - a}{n} = \frac{6 - 1}{5} = 1$

Step 2 ：Calculate the $x_{i}$ values: $x_{0} = 1 + 0 * 1 = 1$ , $x_{1} = 1 + 1 * 1 = 2$ , $x_{2} = 1 + 2 * 1 = 3$ , $x_{3} = 1 + 3 * 1 = 4$ , $x_{4} = 1 + 4 * 1 = 5$ , $x_{5} = 1 + 5 * 1 = 6$

Step 3 ：Substitute these $x_{i}$ values into the function $f (x) = \frac{\cos (x)}{x}$ : $f (x_{0}) = \frac{\cos (1)}{1}$ , $f (x_{1}) = \frac{\cos (2)}{2}$ , $f (x_{2}) = \frac{\cos (3)}{3}$ , $f (x_{3}) = \frac{\cos (4)}{4}$ , $f (x_{4}) = \frac{\cos (5)}{5}$ , $f (x_{5}) = \frac{\cos (6)}{6}$

Step 4 ：Substitute these values into the trapezoidal rule formula: $\int_{1}^{6} \frac{\cos (x)}{x} d x \approx \frac{1}{2} [\frac{\cos (1)}{1} + 2 * \frac{\cos (2)}{2} + 2 * \frac{\cos (3)}{3} + 2 * \frac{\cos (4)}{4} + 2 * \frac{\cos (5)}{5} + \frac{\cos (6)}{6}]$

Use the trapezoidal rule with n=5 to approximate∫16cos⁡(x)xdx

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Use the trapezoidal rule with $n = 5$ to approximate
$\int_{1}^{6} \frac{\cos (x)}{x} d x$