If f ( x ) ex 6 , 0 x 2 , find the Riemann sum with n 4 correct to six decimal places, taking the sample points to be midpoints Step 1 We must calculate M 4 4 f xi x f x 1 f x 2 f x 3 f x 4 xi 1 , where x 1 , x 2 , x 3 , and x 4 represent the midpoints of four equal subintervals of 0 , 2 Since we wish to estimate the area over the interval 0 , 2 using 4 rectangles of equal widths, then each rectangle will have width x 1 2 1 2 Step 2 We wish to find M 4 1 2 f x 1 f x 2 f x 3 f x 4 Since x 1 , x 2 , x 3 , and x 4 represent the midpoints of the four sub intervals of 0 , 2 , then we must have the following x 1 x 2 x 3 x 4

Question

If f ( x )   ex 6 , 0 x 2 , find the Riemann sum with n   4 correct to six decimal places, taking the sample points to be midpoints  Step 1 We must calculate M 4   4 f xi x   f x 1   f x 2   f x 3   f x 4 xi   1 , where x 1 , x 2 , x 3 , and x 4 represent the midpoints of four equal subintervals of   0 , 2     Since we wish to estimate the area over the interval   0 , 2   using 4 rectangles of equal widths, then each rectangle will have width x   1   2 1   2   Step 2 We wish to find M 4   1 2 f x 1   f x 2   f x 3   f x 4   Since x 1 , x 2 , x 3 , and x 4 represent the midpoints of the four sub   intervals of   0 , 2   , then we must have the following  x 1   x 2   x 3   x 4

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If f ( x ) = ex 6 , 0 x 2 , find the Riemann sum with n = 4 correct to six decimal

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