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Trapezoid Rule

shamieh

Active member
Sep 13, 2013
539
Just need someone to verify my solution and that I have done my calculations correctly. Thank you again for all of your help in advance, everyone on this forum has helped me SO much with my classes this semester.

Using the trapezoid rule.

The following data was collected about the function \(\displaystyle f(x)\)

Estimate \(\displaystyle \int^{1.25}_0 f(x) \, dx\)

\(\displaystyle x | f(x)\)

\(\displaystyle 0 | 3.000\)

\(\displaystyle .25 | 2.540\)

\(\displaystyle .50 | 1.583\)

\(\displaystyle .75 | 1.010\)

\(\displaystyle 1.00 | 1.346\)

\(\displaystyle 1.25 | 2.284\)

I ended up with \(\displaystyle .25[3.000 + 2(2.540) + 2(1.583) + 2(1.010) + 2(1.346) + 2.284] \approx 4.5605\)
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
The constant in front should be:

\(\displaystyle \frac{b-a}{2n}=\frac{1.25-0}{2\cdot5}=0.125\)

Your result is twice as large as it should be. :D
 

shamieh

Active member
Sep 13, 2013
539
The constant in front should be:

\(\displaystyle \frac{b-a}{2n}=\frac{1.25-0}{2\cdot5}=0.125\)

Your result is twice as large as it should be. :D
I knew something didn't look right...lol
Thanks Mark!

- - - Updated - - -

so does $\approx 2.28025$ look more accurate?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Yes, that looks good. :D