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Riemann Sums

Riemann Sums. Jim Wang Mr. Brose Period 6. Approximate the Area under y = x² on [ 0,4 ]. 4 rectangles whose height is given using the left endpoint 4 rectangles whose height is given using the right endpoint 4 rectangles whose height is given using the midpoint 4 trapezoids

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Riemann Sums

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  1. Riemann Sums Jim Wang Mr. Brose Period 6

  2. Approximate the Area undery = x² on [ 0,4 ] • 4 rectangles whose height is given using the left endpoint • 4 rectangles whose height is given using the right endpoint • 4 rectangles whose height is given using the midpoint • 4 trapezoids • Evaluate the integral directly

  3. a) 4 rectangles whose height is given using the left endpoint Left: ( b • h ) (1)0 + (1)1 + (1)4 + (1)9 1 2 3 4 Ans. = 14

  4. b) 4 rectangles whose height is given using the right endpoint Right: ( b • h ) (1)1 + (1)4 + (1)9 + (1)16 1 2 3 4 Ans. = 30

  5. c) 4 rectangles whose height is given using the midpoint Midpoint: ( b • h) (1)1/4 + (1)9/4 + (1)25/4 + (1)49 1 2 3 4 Ans. = 84/4 or 21

  6. d) 4 trapezoids Area of Trapezoid: ½ h ( b1 + b2 ) ½ (1) [ 0+1 + 1+4 + 4+9 + 9+16 ] 1 2 3 4 ½ [ 44 ] Ans. = 22

  7. e) Evaluate the integral directly Insert in Calculator: f(x) = 04x² dx Ans. = 64/3

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