Trapezoidal and Simpson's Rule

[Johnmoon]

Hello, I am having trouble with these two problems. If there's any chance I could get some suggestions as to where my calculations are wrong please don't hesitate to respond. Thank you
Since there has to be 6 trapezoids I choose the numbers 1, 7/6, 4/3, 3/2, 5/3, 11/6, and 2 as the x points and when I put them into the function and multiply everyone, but 1 and 2 by 2, I end up with these numbers. Please let me know what the answers are along with how to obtain them. Thank you.

 

[ksdhart2]

Your answers are very very close to what I got. For the trapezoid rule, I came up with \(\displaystyle \int\limits_{x=1}^{2} \frac{1}{x} \: dx \approx 0.6948{\color{red}77}\) and for Simpson's rule, I came up with \(\displaystyle \int\limits_{x=1}^{2} \frac{1}{x} \: dx \approx 0.6931{\color{red}49}\)

The answers are so close that it may well be due to a rounding error, but I can't wholly dismiss the possibility of a math error without seeing all of your calculations.

 

[tkhunny]

Round all answers to six decimal places

is NOT the same as

Round all intermediate values to six decimal places.