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Section 5.2 Area Phong Chau

Section 5.2 Area Phong Chau. 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 5.2 Area Phong Chau

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  1. Section 5.2 AreaPhongChau

  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. SummationNotation The sum of n terms can be written using sigma notation: where i is the index of summation 1 is the lower bound n is the upper bound Example:

  4. Summation Formulas

  5. Example • Evaluate

  6. Estimating Areas A≈A1 + A2 + A3 + A4 A1 A2 A3 A4 | a | b

  7. Determining Ai A1 A2 A3 A4 | a | b x1 x2 x3 x4

  8. 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

  9. Examples • Find the area of the region bounded by the graph of f(x) = 3x, the x-axis and the vertical lines x = 1 and x = 6, using • Geometry Formula • The limit Definition of Area

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