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Math Help - [SOLVED] Evaluate the Indefinite Integral

  1. #1
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    [SOLVED] Evaluate the Indefinite Integral

    Hi,
    I'm I on the right track with this problem?

    1. The problem statement, all variables and given/known data
    Evaluate the Indefinite Integral


    2. Relevant equations
    integral of sin t sec^2 (cos t)dt


    3. The attempt at a solution
    integral of sin t sec^2 (cos t)dt

    Let u = cos t

    du/dt = sin t

    dt * -sin t = du

    dt = du/-sin t

    integral sin t sec^2 (u) dt

    integral sin t sec^2 (u) du/-sin t

    - integral of sec^2 (u) du

    - [tan (u) du ] + c

    - tan (cos t) + c
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  2. #2
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by sparky View Post
    Hi,
    I'm I on the right track with this problem?

    1. The problem statement, all variables and given/known data
    Evaluate the Indefinite Integral


    2. Relevant equations
    integral of sin t sec^2 (cos t)dt


    3. The attempt at a solution
    integral of sin t sec^2 (cos t)dt

    Let u = cos t

    du/dt = -sin t

    dt * -sin t = du

    dt = du/-sin t

    integral sin t sec^2 (u) dt

    integral sin t sec^2 (u) du/-sin t

    - integral of sec^2 (u) du

    - [tan (u) du ] + c

    - tan (cos t) + c
    All correct except for the line with red color. It must be a typo! \frac{d (cost)}{dt}= -sint
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  3. #3
    MHF Contributor
    skeeter's Avatar
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    North Texas
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    Quote Originally Posted by sparky View Post
    Hi,
    I'm I on the right track with this problem?

    1. The problem statement, all variables and given/known data
    Evaluate the Indefinite Integral


    2. Relevant equations
    integral of sin t sec^2 (cos t)dt


    3. The attempt at a solution
    integral of sin t sec^2 (cos t)dt

    Let u = cos t

    du/dt = sin t

    dt * -sin t = du

    dt = du/-sin t

    integral sin t sec^2 (u) dt

    integral sin t sec^2 (u) du/-sin t

    - integral of sec^2 (u) du

    - [tan (u) du ] + c

    - tan (cos t) + c
    differentiate your result to check the work.
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  4. #4
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    Quote Originally Posted by harish21 View Post
    All correct except for the line with red color. It must be a typo! \frac{d (cost)}{dt}= -sint
    Ok, thanks very much skeeter and harish21
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