Calculus 2 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.) , n=6

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Step-by-step explanation:

We want to estimate the definite integral:

Using the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule with six equal subdivisions.

1)

The trapezoidal rule is given by:

Our limits of integration are from x = 1 to x = 4. With six equal subdivisions, each subdivision will measure:

Therefore, the trapezoidal approximation is:

Evaluate:

2)

The midpoint rule is given by:

Thus:

Simplify:

3)

Simpson's Rule is given by:

So:

Simplify:

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step-by-step explanation: