Check my answer to a Trapezoid rule question?

• Feb 24th 2014, 06:27 PM
canyouhelp
Check my answer to a Trapezoid rule question?
This is for an online practice quiz for participation points, but I'm not completely sure about my answer but I chose the option that was closest. Is this right?

http://i61.tinypic.com/nn9xzc.jpg
• Feb 24th 2014, 07:04 PM
ibdutt
Re: Check my answer to a Trapezoid rule question?
You must post the calculations you have done
• Feb 25th 2014, 06:43 AM
canyouhelp
Re: Check my answer to a Trapezoid rule question?
Okay.. I just re-did my calculations because I didn't save them the first time. This time I got about 6. To do this I averaged the height of each trapezoid and the multiplied that by two (the width.) Do I need to type in each one I did? I know I'm wrong because it's too low. What am I doing wrong? I drew the trapezoids, added the two lengths/2*2 and added each of those individually and only got 6. :(
• Feb 25th 2014, 09:13 AM
hollywood
Re: Check my answer to a Trapezoid rule question?
You didn't mention setting up the integral. It's not just the integral of the function - you need to calculate the arc length.

Each trapezoid is 1/4 wide, since there are eight of them and they span from x=0 to x=2. The exact value of the integral is about 13.965, so if you're getting 6, there's something wrong.

- Hollywood
• Feb 25th 2014, 10:49 AM
canyouhelp
Re: Check my answer to a Trapezoid rule question?
Quote:

Originally Posted by hollywood
You didn't mention setting up the integral. It's not just the integral of the function - you need to calculate the arc length.

Each trapezoid is 1/4 wide, since there are eight of them and they span from x=0 to x=2. The exact value of the integral is about 13.965, so if you're getting 6, there's something wrong.

- Hollywood

Okay, you're right. I set it up right the first time but not the second. But 13.965 doesn't even match any of the answers. Why is this?
• Feb 25th 2014, 06:34 PM
hollywood
Re: Check my answer to a Trapezoid rule question?
You're estimating the value using the trapezoidal rule, not calculating the exact value.

- Hollywood
• Feb 26th 2014, 07:31 AM
canyouhelp
Re: Check my answer to a Trapezoid rule question?
Quote:

Originally Posted by hollywood
You're estimating the value using the trapezoidal rule, not calculating the exact value.

- Hollywood

Oh, I'm not sure how to estimate instead of just doing it normally. How would you estimate that? It's easier to just find it exactly!
• Feb 26th 2014, 09:35 AM
johng
Re: Check my answer to a Trapezoid rule question?
The attachment has a discussion of the trapezoid rule in general and your specific problem as an example. From the choice of answers given, the correct answer is c) 14.093. Your comment about computing the exact value of the integral is easier is a little suspect. Try computing the integral for the arc length; it's not that easy. Finally, if you Google "trapezoid rule calculator", you'll find a lot of sites that will do the arithmetic for you, and thus check your work.

Attachment 30255
• Feb 26th 2014, 09:49 AM
canyouhelp
Re: Check my answer to a Trapezoid rule question?
Quote:

Originally Posted by johng
The attachment has a discussion of the trapezoid rule in general and your specific problem as an example. From the choice of answers given, the correct answer is c) 14.093. Your comment about computing the exact value of the integral is easier is a little suspect. Try computing the integral for the arc length; it's not that easy. Finally, if you Google "trapezoid rule calculator", you'll find a lot of sites that will do the arithmetic for you, and thus check your work.

Attachment 30255

Alright, thank you. I like to draw it out and then use trapezoids, so maybe it's not that exact but I think it's easier than all the arithmetic, but you're right I have a lot of trouble with exactness for arc length.