Step 1:

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The function is $\"\"$ .

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Consider the function as $\"\"$

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Fid the fourth derivative of $\"\"$ .

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Differentiate with respect to $\"\"$ .

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$\"\"$

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Differentiate with respect to $\"\"$ .

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$\"\"$

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Differentiate with respect to $\"\"$ .

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$\"\"$

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Again differentiate with respect to $\"\"$ .

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$\"\"$

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It is obvious that $\"\"$ is increasing and it has the absolute maximum in the interval $\"\"$ at $\"\"$ .

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Consider the number $\"\"$

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Find the number $\"\"$ using Simpsons error formula.

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Simpsons error formula is: $\"\"$ .

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Substitute $\"\"$ , $\"\"$ in above formula.

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$\"\"$

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Here error less than $\"\"$ .

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Determine $\"\"$ with the error less than $\"\"$ .

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$\"\"$

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Solution:

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Approximate value of $\"\"$ is 40.