$\"\"$

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The function $\"\"$ is a linear function.

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Consider $\"\"$ on interval $\"\"$ .

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The definite integral is $\"\"$ .

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Describe the size of error when the Trapezoidal Rule is used to approximate $\"\"$ .

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If $\"image\"$ has a continuous second derivative on $\"\"$ , then the error approximating the integral $\"\"$ by Trapezoidal Rule is $\"\"$ , $\"\"$ .

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The definite integral is $\"\"$ .

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$\"\"$

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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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The error approximating the integral is $\"\"$ .

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In this case $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$ .

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The size of error is zero because the Trapezoidal Rule always perfectly fit under a linear function.

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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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The Trapezoidal Rule perfectly fits a linear function.

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$\"\"$

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The size of error is zero because the Trapezoidal Rule always perfectly fit under a linear function.

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

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$\"\"$ .