Unformatted text preview: 1 and x 2 is (x 1 + x 2 ). 3. Find the height of each rectangle. Evaluate the sample point in f(x) to determine the height of the rectangle. 4. Find the area of each rectangle. Multiply the height of the rectangle by the length to get the area. 5. Use the areas of all the rectangles to approximate the area under the curve. Total the areas of all the rectangles to get an approximation of the area under the curve y = x 2 , over the interval [2, 11]. Our approximate area is 434.25. Subinterval Sample Pt X i * Height of Rectangle f(X i *) Length of Rectangle ∆x Area of Rectangle f(X i *)∆x [2 , 5 ] X 1 * = .5(2 + 5 ) X 1 * = 3.5 f(3.5) = (3.5) 2 3 (3.5) 2 (3) = 36.75 [5, 8] X 2 * = .5(5 + 8) X 2 * = 6.5 f(6.5) = (6.5) 2 3 (6.5) 2 (3) = 126.75 [8 11] X 3 * = .5(8 + 11) X 3 * = 9.5 f(9.5) = (9.5) 2 3 (9.5) 2 (3) =270.75 TOTAL 434.25...
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 Fall '11
 Augustarainsford
 Height, Rectangle, Riemann sum

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