is my n correct?

[Ryan Rigdon]

is my n correct in this problem.

 

[BigGlenntheHeavy]

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

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

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

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

\(\displaystyle Hence, \ .68 \ \le \ \int_{2}^{4}\frac{1}{x}dx \ \le \ .70\)

 

[Ryan Rigdon]

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.

 

[BigGlenntheHeavy]

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

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

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

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