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**Section 15.3 Area and Definite Integral**

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Area Estimation How can we estimate the area bounded by the curve y = x2, the lines x = 1 and x = 3, and the x-axis? We will use 4 rectangles to approximate the area. Question How can we improve our estimation?

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**Definition of the Area of a Region**

The area of the region bounded by the graph of f(x), the x-axis, the vertical lines x = a and x = b is where ci is the endpoint of the ith interval, and

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**The Definite Integral The definite integral of f from a to b is**

where a is called lower limit, b is called upper limit, If f(x) is above the x-axis, then the definite integral of f (x) from a to b represents the area of the region bounded by the graph of f(x), the x-axis , the vertical lines x = a and x = b.

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Examples Evaluate the integrals by interpreting in terms of area.

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