$\"\"$

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(a)

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Consider the function concave up on interval $\"\"$ is $\"\"$ .

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Consider the function concave down on interval $\"\"$ is $\"\"$ .

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

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

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$\"\"$ .

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Observe the Graph:

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Using Trapezoidal rule the integral value $\"\"$ .

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The definite 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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Therefore, the Trapezoidal rule is overestimate in $\"\"$ .

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$\"\"$

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

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$\"\"$ .

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Observe the Graph:

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Using Trapezoidal rule the integral value $\"\"$ .

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The definite 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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The Trapezoidal rule is underestimate in $\"\"$ . $\"\"$

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(b)

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Simposons rule.

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Since the two functions are quadratic functions Simpsons rule is more accurate approximations of $\"\"$ and $\"\"$ .

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The Trapezoidal Rule approximates using first degree polynomials(linear).

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$\"\"$

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(a) \ \

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The Trapezoidal rule is overestimate in $\"\"$ .

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The Trapezoidal rule is underestimate in $\"\"$ .

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(b) Simpsons rule.