(adsbygoogle = window.adsbygoogle || []).push({}); Problem statement

Find an approximate value for log(2) by subdividing the interval [1,2] into sub-intervals of length 1/n and using this subdivision to compute the upper sum for the function f(x)=1/x. Compute the upper sum for n=1,2,...,10.

My solution

The way I approached this is as follows

Use the definition of integral: as n -> inf ([tex]\sum[/tex] f(ci)*partition length)

a. take a partition of size 0.1 (as I have 10 points from 1-2)

b. find f(1.0) + f(1.1) + ... f(1.9) = 1/1 + 1/1.1 + 1/1.2 + .... 1/1.9 = 7.185

c. Multiply 7.185*0.1 = 0.7185

Obviously log2 = 0.301 ~= 0.7185/2. <--- Error.

To see if my understanding of integrals is right, I used same method for f(x) =x^2 from [1,2] and came up with the right answer. So what am I doing wrong with 1/x.

Thanks

Asif

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# Homework Help: Log2 - why am I off by 2

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