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Math Help - Not sure about this curve/definite integral question?

  1. #1
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    Not sure about this curve/definite integral question?

    I have a 3 part question and I'm not sure about my answers. Can you help? (It's for an online practice quiz)

    1. http://i61.tinypic.com/2ugcw9c.jpg

    2. http://i58.tinypic.com/346wak9.jpg w/ http://i59.tinypic.com/717bs7.jpg

    3. http://i60.tinypic.com/mjsoi9.jpg

    I'm pretty sure about part 1, but the other two I've spent a long time on and I keep getting different answers. What should I be getting?

    Thanks!
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  2. #2
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    Re: Not sure about this curve/definite integral question?

    For #1, you should have learned an arc length formula - you can just plug in the function and limits to get the answer.

    - Hollywood
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  3. #3
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    Re: Not sure about this curve/definite integral question?

    Quote Originally Posted by hollywood View Post
    For #1, you should have learned an arc length formula - you can just plug in the function and limits to get the answer.

    - Hollywood
    For number one that's what I did. I thought I had that one right. Is it not? I was more worried about the other two parts.
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  4. #4
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    Re: Not sure about this curve/definite integral question?

    I just started with #1. You've posted a lot of questions lately.

    It's a lot easier to look at a solution and see if there's a problem as opposed to solving the problem and comparing results.

    - Hollywood
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  5. #5
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    Re: Not sure about this curve/definite integral question?

    Quote Originally Posted by hollywood View Post
    I just started with #1. You've posted a lot of questions lately.

    It's a lot easier to look at a solution and see if there's a problem as opposed to solving the problem and comparing results.

    - Hollywood
    I know I've posted a lot lately But thanks for helping me so much. It's from a ton of questions that my professor gave us that aren't for a grade but we're all struggling. I've asked other people in the class and they can't figure this one out. Did I get #1 right? Because I was pretty confident about it but now I'm not sure. And I don't even know where to start for the other two. I'm fairly certain I calculated #2 wrong.
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    Re: Not sure about this curve/definite integral question?

    Quote Originally Posted by hollywood View Post
    I just started with #1. You've posted a lot of questions lately.

    It's a lot easier to look at a solution and see if there's a problem as opposed to solving the problem and comparing results.

    - Hollywood
    I just tried to integrate each one over again for part 1. And the last option is about 8.5 when the one in the graph is 1.75. When I graph the options though the graph for the last option matches the graph in the question? Maybe I'm integrating them wrong but none of them ended up being 1.75, and the closest graph is the last one. Is the last one not right even though when I graph it out the graph looks really similar?
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  7. #7
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    Re: Not sure about this curve/definite integral question?

    The formula for arc length is L = \int_a^b \sqrt{1+(y')^2} \, dx. Since y = x^{-2}, y' = -2x^{-3}, so the integrand is \sqrt{1+(-2x^{-3})^2} = \sqrt{1+4x^{-6}}, and the third answer is correct.

    In #2, the fourth answer is correct. You bring \Delta y out of the square root instead of \Delta x.

    In #3, the second answer is correct.

    - Hollywood
    Thanks from canyouhelp
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  8. #8
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    Re: Not sure about this curve/definite integral question?

    Quote Originally Posted by hollywood View Post
    The formula for arc length is L = \int_a^b \sqrt{1+(y')^2} \, dx. Since y = x^{-2}, y' = -2x^{-3}, so the integrand is \sqrt{1+(-2x^{-3})^2} = \sqrt{1+4x^{-6}}, and the third answer is correct.

    In #2, the fourth answer is correct. You bring \Delta y out of the square root instead of \Delta x.

    In #3, the second answer is correct.

    - Hollywood
    Oh okay, I was mixing up arc length with area, oops. I'll have to have my professor go into depth about the other two but thank you!
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