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Math Help - Another one to integrate

  1. #1
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    Another one to integrate

    1.)
    Answer Key:


    2.)
    Answer Key:


    Thanks a lot!!!!
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  2. #2
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    Here's the first one

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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
    1.)
    Answer Key:


    2.)
    Answer Key:


    Thanks a lot!!!!
    um, for the second one, i think you gave the answer key twice
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  4. #4
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    sory for the typo

    The question is
    integral of sin(x)*(sin(cosx))dx
    answer key: (cos(cos(x)) + C
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Krizalid View Post
    Here's the first one

    that's nice. i didn't even consider substitution. i ended up trying trig substitution, which was hell. but things seemed to be working out nicely until i ended up with x^4/4(x^2 + 4)^2 which is wrong.
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  6. #6
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    The question is
    integral of sin(x)*(sin(cosx))dx
    This is a really easy one

    Just set u = cos x and du = - sin x dx, therefore the integral becomes to -sin udu, which yields cos u + c and we've got that cos (cos x) + c.
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  7. #7
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    The question is
    integral of sin(x)*(sin(cosx))dx
    answer key: (cos(cos(x)) + C
    we proceed by substitution:

    let u = cos(x)
    => du = -sin(x) dx
    => - du = sin(x) dx
    so our integral becomes:

    - int{sin(u)}du = cos(u) + C = cos(cos(x)) + C


    too late
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