The Definite Integral. In the previous section, we approximated area using rectangles with specific widths. If we could fit thousands of “partitions”

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Presentation transcript:

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.

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

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 :

The Definite Integral EXAMPLE # 1 : Find

The Definite Integral EXAMPLE # 1 : Find

The Definite Integral EXAMPLE # 1 : Find

The Definite Integral EXAMPLE # 1 : Find

The Definite Integral EXAMPLE # 1 : Find

The Definite Integral EXAMPLE # 2 : Find

The Definite Integral EXAMPLE # 2 : Find

The Definite Integral EXAMPLE # 2 : Find

The Definite Integral EXAMPLE # 2 : Find

The Definite Integral

EXAMPLE # 3 : Evaluate

The Definite Integral EXAMPLE # 3 : Evaluate

The Definite Integral EXAMPLE # 3 : Evaluate

The Definite Integral EXAMPLE # 3 : Evaluate

The Definite Integral EXAMPLE # 3 : Evaluate

The Definite Integral EXAMPLE # 3 : Evaluate