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3 years ago

Midpoint rule with given value

Mathematics

1 answer:

jeyben [28]3 years ago

5 0

9514 1404 393

Answer:

M₅ = 1.6570

Step-by-step explanation:

The basic idea is to find the function values at x ∈ {1.1, 1.3, 1.5, 1.7, 1.9}, add those values, and multiply the result by 1/5. Those x-values are the midpoints of intervals 0.2 units wide, between x = 1 and x = 2. The width 0.2 is the total interval width (2-1=1) divided by n = 5.

The calculation and results are shown in the attachment. Rounded to 4 decimal places, the integral is ...

M₅ = 1.6570

The actual integral is about 1.6574, so this is pretty close.

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