$\"\"$

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The integral is $\"\"$ , $\"\"$ .

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Consider $\"\"$ .

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In this case $\"\"$ .

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Width $\"\"$

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Substitute $\"\"$ and $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Find the function values.

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ values in $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ . $\"\"$

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Trapezoidal rule:

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$\"\"$ . $\"\"$

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Substitute $\"\"$ , $\"\"$ , $\"\"$ , $\"\"$ 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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$\"\"$

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Simpsons rule:

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$\"\"$ .

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$\"\"$

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Substitute $\"\"$ , $\"\"$ , $\"\"$ , $\"\"$ 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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$\"\"$

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The integral is $\"\"$ .

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Let $\"\"$

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

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$\"\"$

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$ Trapezoidal Simpsons Exact

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$\"\"$ $\"\"$ $\"\"$ .