Use simpson's rule with n = 10 to estimate the arc length of the curve. compare your answer with the value of the integral produced by your calculator. (round your answers to six decimal places.) y = ln(6 + x3), 0 ≤ x ≤ 5

Using Simpson's Rule with n = 10 to estimate the arc length of the curve. The value of the integral produced is 8.986792. The value of produced by my graphing calculator is 5.990861.

Let's consider the given function;

The arc length (L) can be computed by using the formula:

Since the interval varies from 0 to 5,

Then, the integral for the arc length will be;

Let us assume that arc length (L) can be written as:

where,

The resolution of the arc length can be given as:

However, intervals of can be expressed as:

Now, by applying Simpson's rule;

L = 8.986792 to six decimal places

L = 5.99086027171

L = 5.990861

Therefore, we can conclude that the value of the integral produced is 8.986792, the value of produced by my graphing calculator is 5.990861.

Learn more about Simpson's rule here:

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The arc length of the curve is

which has a value of about 5.99086.

Let . Split up the interval of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]

The left and right endpoints are given respectively by the sequences,

with .

These subintervals have midpoints given by

Over each subinterval, we approximate with the quadratic polynomial

so that the integral we want to find can be estimated as

It turns out that

so that the arc length is approximately

the answer is a

step-by-step explanation: