$\"\"$

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

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Let $\"\"$ .

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Where $\"\"$ .

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Width $\"\"$

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

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

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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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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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Verify the integral value by using graph:

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Graph the function: $\"\"$ on $\"\"$ and $\"\"$ . $\"\"$ .

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$\"\"$ Trapezoidal Simpsons Graphical Utility

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