Approximating ln using integrals.

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SUMMARY

The discussion focuses on approximating the natural logarithm function, specifically ln(1.5), using integrals. The integral from 1 to 1.5 of dt/t is utilized, along with the approximation formula 1/2 [Lf(P) + Uf(P)], where P represents partition points. Participants clarify that Lf(P) and Uf(P) refer to the lower and upper Riemann sums, respectively, which correspond to left-hand and right-hand sums in this context. The conversation highlights the importance of understanding these concepts for accurate approximation.

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zingoria
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I am not sure how would I work this problem.
Any help would be appreciated.

Estimate
ln 1. 5 = Integral from 1 to 1.5 dt/t
using the approximation 1
2 [Lf (P) + Uf (P)] with
P = {1 =8/8, 9/8, 10/8, 11/8, 12/8=1.5}
 
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what are Lf(P), Uf(P), are they just two diffrent functions, or?
if they are functions do they hve any other property given?
 
They mean Riemann sums with Lower/Upper function values. In this case, it correspondes to Left hand/Right hand sums.

I don't understand zingorias 3rd last and last line very well, what exactly have you tried so far?

PS- This should have been posted in a homework forum.
 

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