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Thread: Spot the error

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    Default Spot the error

    Hiya!
    Working on some stupid calculus test and I'm making a very stupid mistake. Unfortunately, I can't find the error (I do know the right way which is to chose the cosine as u but I want to know why my method is wrong as I'll never be smart enough to actually use that).


    Let be u, then
    So the integral becomes which turns out to be zero, yay! Real answer: 4/3.
    My error most likely is at the part where I pick u, but I don't know WHY it is wrong Anyone who can take a minute to explain please?
    Last edited by Markus; 04-14-2013 at 08:42 PM.

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    sin isn't capitalised. Chicks love the capitalised Sin

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    I managed 2/3. Give me a minute and I'll have another shot.

    EDIT: Got it. I'll upload a pic of my working.
    Last edited by Rich; 04-14-2013 at 09:21 PM.
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    I don't know calculus but I do know that 1-cosĀ²=sinĀ². Maybe that helps?

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    found this http://answers.yahoo.com/question/in...6021501AANSlj0

    you should also be able to convert coordinate systems aswell

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    Cheeky bit of round 1 underneath as well
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    My attempt. Also stranded at 0. I don't understand what you did Rich. Will look into it tomorrow.


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    Yours all makes sense until you actually integrate your (-1+a^2)a'. You'd have to use some method of integration to do that other than by inspection/recognition because you have two functions of a multiplied together, whereas you've integrated those functions separately then multiplied them.
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    Quote Originally Posted by Rich View Post
    Yours all makes sense until you actually integrate your (-1+a^2)a'. You'd have to use some method of integration to do that other than by inspection/recognition because you have two functions of a multiplied together, whereas you've integrated those functions separately then multiplied them.
    found it: a' is the same as da

    so it would just disappear. Also it ain't 2/3 but 1/3.

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    Quote Originally Posted by masterBB View Post
    found it: a' is the same as da

    so it would just disappear. Also it ain't 2/3 but 1/3.

    #SillyMistakes #IAmNotGoodInMath #IDontEvenUseTwitter
    Doesn't a'= -sin(x), or have I misunderstood?
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    Quote Originally Posted by Rich View Post
    Doesn't a'= -sin(x), or have I misunderstood?
    Final calculation:




    e:
    Except for the last 0, that has to be 4/3
    Last edited by masterBB; 04-14-2013 at 11:03 PM.
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    Ah fair enough, we've obviously been taught different ways to handle these sorts of questions.
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    Quote Originally Posted by Rich View Post
    Ah fair enough, we've obviously been taught different ways to handle these sorts of questions.
    I am self-taught.

    how is this called:
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    Quote Originally Posted by masterBB View Post
    I am self-taught.

    how is this called:
    Oh wow. Impressive. And that's just a forumla we've been taught to use when integrating by parts. Check this out if it's new to you: http://www.mathsrevision.net/alevel/pages.php?page=19
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    yea, if you got the function h(x) = f(x)*g(x), then H(x) = F(x)*g(x) - ?F(x)*g'(x) dx. +c.

    The lame thing is, if I actually do the deriviation it does make sense:


    So my question remains: why is picking a = (1-cosĀ²x) wrong?

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    Quote Originally Posted by Markus View Post
    So my question remains: why is picking a = (1-cosĀ²x) wrong?
    Because the derivative of 1-cosĀ²(x) is 2cos(x)sin(x), which doesn't help you at all when substituting. You have to integrate by parts in this question.
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    YES! That's the mistake I was looking for. Thanks!

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    Quote Originally Posted by Markus View Post
    YES! That's the mistake I was looking for. Thanks!
    I also was able to do it with a default integral:

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    i see that i am too late

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    Next one!
    Find the work done by the force field F = (x+y)i + (x-z)j + (z-y)k in moving an object from (-1, 0, 1) to (0, -2, 3) along any smooth curve.
    Hint: the correct answer is 19/2!

    My (wrong) approach:
    I made a new script, check it out!.

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    That one's beyond me. I haven't done anything to do with force fields and smooth curves, and since they're not on my syllabus I won't be doing them any time soon. Any idea @masterBB?
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