$\"\"$

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The function is $\"\"$ .

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(a) Determine $\"\"$ by Midpoint Rule:

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

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Number of subintervals are $\"\"$ .

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Width of the interval : $\"\"$ .

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$\"\"$ , where $\"\"$ .

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$\"\"$ .

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Mid points are $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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Find the integral value by integration by parts method.

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$\"\"$

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$\"\"$

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$\"\"$

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Error is $\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(b) Determine $\"\"$ by Simpsons rule:

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The Simpsons rule for approximating $\"\"$ is given by $\"\"$ ,

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where $\"\"$ and $\"\"$ . $\"\"$

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$\"\"$

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$\"\"$ .

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Error is $\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(a) $\"\"$ , $\"\"$ .

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(b) $\"\"$ , $\"\"$ .