is my n correct?

n = 5 is correct.\displaystyle n \ = \ 5 \ is \ correct.

241xdx =˙ .69314718056, (TI89)\displaystyle \int_{2}^{4}\frac{1}{x}dx \ \dot= \ .69314718056, \ (TI-89)

Trapezoid Rule when n = 5\displaystyle Trapezoid \ Rule \ when \ n \ = \ 5

241xdx = 15[1/2+5/6+5/7+5/8+5/9+1/4] =˙ .695634920635\displaystyle \int_{2}^{4}\frac{1}{x}dx \ = \ \frac{1}{5}[1/2+5/6+5/7+5/8+5/9+1/4] \ \dot= \ .695634920635

Hence, .68  241xdx  .70\displaystyle Hence, \ .68 \ \le \ \int_{2}^{4}\frac{1}{x}dx \ \le \ .70
 
i got the same answer as you. had to round off to three decimal places. thought you would like to see my work. thanx for the help again.
 

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You are welcome, good show.\displaystyle You \ are \ welcome, \ good \ show.

Note, when n = 6, Simpsons Rule:\displaystyle Note, \ when \ n \ = \ 6, \ Simpson's \ Rule:

241xdx = 19[1/2+12/7+3/4+4/3+3/5+12/11+1/4] =˙ .693167979317\displaystyle \int_{2}^{4}\frac{1}{x}dx \ = \ \frac{1}{9}[1/2+12/7+3/4+4/3+3/5+12/11+1/4] \ \dot= \ .693167979317

An error of only .69314718056.693167979317 = .00003255044.\displaystyle An \ error \ of \ only \ .69314718056-.693167979317 \ = \ -.00003255044.
 
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