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Section 15.3 Area and Definite Integral

Section 15.3 Area and Definite Integral. Area Estimation. How can we estimate the area bounded by the curve y = x 2 , 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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Section 15.3 Area and Definite Integral

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  1. Section 15.3 Area and Definite Integral

  2. 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? http://science.kennesaw.edu/~plaval/applets/Riemann.html

  3. 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 ciis the endpoint of the ith interval, and

  4. The Definite Integral • The definite integral of f from a to bis • 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.

  5. Examples Evaluate the integrals by interpreting in terms of area.

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