$\"\"$

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Observe the table:

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The number of subintervals are $\"\"$ .

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The function values are $\"\"$ , $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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(a) Approximate the integral $\"\"$ using the Trapezoidal Rule.

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Trapezoidal 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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Using the Trapezoidal rule $\"\"$ . $\"\"$ Approximate the integral $\"\"$ using the Simpsons Rule.

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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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Using the Simpsons Rule $\"\"$ . $\"\"$

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(b)

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Graph:

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Plot the points: $\"\"$ ,

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

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Draw the curve.

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$\"\"$ .

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By graphing utility, the equation is $\"\"$ .

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$\"\"$

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The integral is $\"\"$ .

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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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$\"\"$

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$\"\"$

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$\"\"$ .

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

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(a)

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Trapezoidal Rule $\"\"$ .

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Simpsons Rule $\"\"$ .

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(b) The equation is $\"\"$ .

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$\"\"$ .