mares-riemann-sum

# mares-riemann-sum - Use the midpoint method to estimate âˆ...

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Sheet1 Page 1 variable meaning formula n # of rectangles 10 a left endpoint 0 b right endpoint 2 Δx width of a rectangle (b-a)/n 0.2 i just a label 1 2 3 4 5 6 7 xi Right-side of rectangle #i a + i Δx 0.2 0.4 0.6 0.8 1 1.2 1.4 xi* sample point (midpoint) 0.1 0.3 0.5 0.7 0.9 1.1 1.3 height of rectangle #i f(xi*) 0.01 0.09 0.25 0.49 0.81 1.21 1.69 area of rectangle #i f(xi*) Δx 0 0.02 0.05 0.1 0.16 0.24 0.34 total area Σ f(xi*) Δx 2.6600 Cumulative area of rect's: 0 0.02 0.07 0.17 0.33 0.57 0.91 Above line estimates g(xi): g(xi) Approximate the derivative of g(x): is approximately: 0.01 0.09 0.25 0.49 0.81 1.21 1.69 Compare this line ^^^ with f(xi*

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Unformatted text preview: Use the midpoint method to estimate âˆ« 2 x 2 Î”x with ten rectangles ( x i-1 + x i ) / 2 Î£ i j=1 f(xj*) Î”x âˆ« 0.2 x 2 dx âˆ« 0.6 x 2 dx âˆ« 1 x 2 dx âˆ« 1.4 x 2 d âˆ« xi t 2 dt âˆ« 0.2 t 2 dt âˆ« 0.6 t 2 dt âˆ« 1 t 2 dt âˆ« 1.4 t 2 dt (g(x i ) â€“ g(x i-1 )) / Î”x Sheet1 Page 2 8 9 10 1.6 1.8 2 1.5 1.7 1.9 2.25 2.89 3.61 0.45 0.58 0.72 1.36 1.94 2.66 2.25 2.89 3.61 i*) !!! dx âˆ« 2 x 2 dx t âˆ« 2 t 2 dt...
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mares-riemann-sum - Use the midpoint method to estimate âˆ...

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