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Given the table below for selected values of f(x), use 6 trapezoids to estimate the value of x 1 3 4 6 7 9 10 f(x) 4 8 6 10 10...Asked by Jim
2) Given the table below for selected values of f(x), use 6 trapezoids to estimate the value of (10)∫(1) f(x)dx
x 1 3 4 6 7 9 10
f(x) 4 8 6 10 10 12 16
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Answered by
Steve
you have the values. Just compute the area of the kth trapezoid using
a<sub><sub>k</sub></sub> = (f(x<sub><sub>k</sub></sub>)+f(x<sub><sub>k+1</sub></sub>))/2 * (x<sub><sub>k+1</sub></sub>-x<sub><sub>k</sub></sub>) for k=1..6
For example, a<sub><sub>1</sub></sub> = (4+8)/2 * (3-1) = 12
a<sub><sub>k</sub></sub> = (f(x<sub><sub>k</sub></sub>)+f(x<sub><sub>k+1</sub></sub>))/2 * (x<sub><sub>k+1</sub></sub>-x<sub><sub>k</sub></sub>) for k=1..6
For example, a<sub><sub>1</sub></sub> = (4+8)/2 * (3-1) = 12
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