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Math Help - trigonometric integrals help

  1. #1
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    trigonometric integrals help

    pls help me solve this difficult integral i cant easily solve:

    the answer is -2cot(2x)+C
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    pls help me solve this difficult integral i cant easily solve:

    the answer is -2cot(2x)+C
    Write out,

    (1/sin^4 x)/(cos^2 x/sin^2 x) = 1/(sin^2 x cos^2 x)

    =1/(sin x cos x)^2 = 4 * 1/(2 sin x cos x)^2 = 4 * 1/(sin 2x)^2

    = 4*csc^2(2x)

    Thus, it simplify to,

    4*INT csc^2 (2x) dx

    Use the substitution t=2x and the fact that INT csc^2 t dt = -cot^2 t+C
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    pls help me solve this difficult integral i cant easily solve:

    the answer is -2cot(2x)+C
    I was worried i got the wrong answer but it turns out to be the same thing. use what TPH said, my way requires some revision in trig proofs
    Attached Thumbnails Attached Thumbnails trigonometric integrals help-int.gif  
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  4. #4
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    thank you!
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  5. #5
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    Re:

    RE:

    If I wanted to evaluate this problem using Maplesoft how would I go about doing it?
    Attached Thumbnails Attached Thumbnails trigonometric integrals help-maplesoft.gif  
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by qbkr21 View Post
    RE:

    If I wanted to evaluate this problem using Maplesoft how would I go about doing it?
    i don't see how it got that ln answer so i'd go with the second one. you should be able to prove it is the same answer above using trig identities

    Maple is a nice utility though, so you can have faith that you'll get the right answer if you type the question correctly
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  7. #7
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    Re:

    Re:

    So you think that second answer using "Evaluate" is the same?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by qbkr21 View Post
    Re:

    So you think that second answer using "Evaluate" is the same?
    I think both answers are right. i don't see maple having trouble with a problem like this. it's just that i can't see how they got the first one. but yes, the second answer i can see is the same. Here:
    Attached Thumbnails Attached Thumbnails trigonometric integrals help-change.gif  
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  9. #9
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    Re:

    There has got to be some simple common denominator feature on this software though...
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  10. #10
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by qbkr21 View Post
    There has got to be some simple common denominator feature on this software though...
    i'm pretty sure there is, but i don't know much about maple...well, i don't remember any of it. we used it when i was doing calc 1 and 2, but when i transfered to my current school, they used MatLab, so i forgot about maple

    (i pretty much forgot about MatLab as well, so don't ask me anything about that. i forgot it quickly because i don't like it, i hate the interface, it is generally more powerful than maple though)
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  11. #11
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    Re:

    Which one is better? User Friendly?
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  12. #12
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by qbkr21 View Post
    Which one is better? User Friendly?
    maple is definately more user friendly. but as i said, MatLab is more powerful. you won't notice the difference in power dealing with basic stuff, but for calc 3 and above, MatLab excels
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