(1)

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Step 1:

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The integral is $\"\"$ .

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Number of sub intervals $\"\"$ .

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Error of bounds for Trapezoidal Rule :

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Suppose $\"\"$ , for $\"\"$ .If $\"\"$ is the error in the mid point rule, then $\"\"$ .

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Here $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Since $\"\"$ , $\"\"$ .

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Therefore, $\"\"$ .

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Here $\"\"$ .

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ in above expression.

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$\"\"$

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$\"\"$

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Upper bound for the $\"\"$ in rectangular mid poit rule is $\"\"$

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Solution :

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Upper bound for the $\"\"$ in rectangular mid poit rule is $\"\"$