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Published byChester Matthews Modified over 6 years ago

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The Definite Integral

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In the previous section, we approximated area using rectangles with specific widths. If we could fit thousands of “partitions” ( rectangles with equal width ) whose width would approach zero into our curve, we would get a very good approximation of the area under this curve.

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The Definite Integral In the previous section, we approximated area using rectangles with specific widths. If we could fit thousands of “partitions” ( rectangles with equal width ) whose width would approach zero into our curve, we would get a very good approximation of the area under this curve. Hence, we could use a summation notation to show this : - as the largest subinterval approaches a zero width

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The Definite Integral In the previous section, we approximated area using rectangles with specific widths. If we could fit thousands of “partitions” ( rectangles with equal width ) whose width would approach zero into our curve, we would get a very good approximation of the area under this curve. Hence, we could use a summation notation to show this : We will simplify this into :

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The Definite Integral EXAMPLE # 1 : Find

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The Definite Integral EXAMPLE # 1 : Find

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The Definite Integral EXAMPLE # 1 : Find

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The Definite Integral EXAMPLE # 1 : Find

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The Definite Integral EXAMPLE # 1 : Find

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The Definite Integral EXAMPLE # 2 : Find

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The Definite Integral EXAMPLE # 2 : Find

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The Definite Integral EXAMPLE # 2 : Find

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The Definite Integral EXAMPLE # 2 : Find

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The Definite Integral

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EXAMPLE # 3 : Evaluate

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The Definite Integral EXAMPLE # 3 : Evaluate

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The Definite Integral EXAMPLE # 3 : Evaluate

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The Definite Integral EXAMPLE # 3 : Evaluate

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The Definite Integral EXAMPLE # 3 : Evaluate

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The Definite Integral EXAMPLE # 3 : Evaluate

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