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Math Help - Check my answer to a Trapezoid rule question?

  1. #1
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    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?

    Last edited by mash; February 24th 2014 at 06:30 PM. Reason: Fixed your image tags
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    Re: Check my answer to a Trapezoid rule question?

    You must post the calculations you have done
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    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.
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    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
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    Re: Check my answer to a Trapezoid rule question?

    Quote Originally Posted by hollywood View Post
    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?
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    Re: Check my answer to a Trapezoid rule question?

    You're estimating the value using the trapezoidal rule, not calculating the exact value.

    - Hollywood
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    Re: Check my answer to a Trapezoid rule question?

    Quote Originally Posted by hollywood View Post
    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!
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    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.

    Check my answer to a Trapezoid rule question?-mhfcalc36.png
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    Re: Check my answer to a Trapezoid rule question?

    Quote Originally Posted by johng View Post
    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.

    Click image for larger version. 

Name:	MHFcalc36.png 
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    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.
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