13_1 Approx Int functions.docx

13_1 Approx Int functions.docx - 13.1 Approximate...

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13.1 Approximate Integration given a Function Approximate the Volume under the Surface of the function f ( x , y ) = 6 x 2 2 y 2 over the region [ 0,2 ] × [ 0,3 ] using ∆ x = ∆ y = 1. y 3 =3 12 13 16 y 2 =2 ¿ 2 3 6 y 1 =1 4 3 0 y 0 =0 6 5 2 x 0 = 0 x 1 =1 x 2 =2 There are six 1x1 rectangles. The height of each rectangle can be given by any of the values of the function at the corner points. Taking the values at each corner and averaging all of them will give us a value of the volume of the function under the curve. 6 4 3 5 2 0
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To see the LHEM/LHEM you choose the points on the lower left hand corner of each rectangle. y 3 =3 12 13 16 y 2 =2 ¿ 2 3 6 y 1 =1 4 3 0 y 0 =0 6 5 2 x 0 = 0 x 1 =1 x 2 =2 Volume = ∆ A f ( x i , y j ) = ¿ 1 * ( f(0,0) + f(0,1) + f(0,2) + f(1,0) + f(1,1) + f(1,3) ) ¿ 1 ( 6 + 4 2 + 5 + 3 3 ) = 13 Notice that only six values are chosen relating to the six rectangles. 6 4 3 5 2 0
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To see the RHEM/RHEM you choose the points on the upper right hand corner of each rectangle.
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  • Fall '16
  • Martin
  • Calculus, Left-handedness, Rectangle, hand corner, The Corner

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