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Math Help - Vol of revolution: Integral of tan(x)

  1. #1
    Junior Member froodles01's Avatar
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    Definite Integral of tan(x)

    I have worked out ∫ tan(x) dx -∏/6<x<∏/3
    to 0.5493 to 4d.p.
    But I'm checking things through & would like some clarification, please.

    Using trig definitions I let tan(x) = sin(x)/cos(x)
    then I used substitution

    let u = cos(x) so du/dx = -sin(x)
    du = -sin(x) dx
    & - du/sin(x) = dx
    -∫ sin(x)/u * du/sin(x) = du/u as sin(x) cancels.
    [-ln(u)] -∏/6<x<∏/3
    =0.5493 to 4d.p.

    Having looked at several other places


    shows that ∫tan(x) = ln(sec(x))+c




    shows the way I did it.

    & my Stroud engineering maths says ∫tan(x) = sec2x
    WolframAlpha gets the same answer as me, too.

    So am I right?
    Last edited by froodles01; March 27th 2012 at 06:49 AM. Reason: Wrong title
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  2. #2
    MHF Contributor
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    Re: Definite Integral of tan(x)

    Your answer is correct.

    Quote Originally Posted by froodles01 View Post
    Having looked at several other places
    ... shows that ∫tan(x) = ln(sec(x))+c

    ... shows the way I did it.
    Indeed, ln(sec(x)) = -ln(cos(x)).

    Quote Originally Posted by froodles01 View Post
    & my Stroud engineering maths says ∫tan(x) = sec2x
    This does not seem to be correct.
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  3. #3
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    Re: Vol of revolution: Integral of tan(x)

    Stroud is wrong. (The derivative of tanx is sec^2x )
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  4. #4
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    Re: Vol of revolution: Integral of tan(x)

    your title says "volume of revolution" ... how did the definite integral of tanx fit into the problem?
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  5. #5
    Junior Member froodles01's Avatar
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    Re: Vol of revolution: Integral of tan(x)

    Title is wrong. I'm doing too many things at once & although I tried to edit this to make title correct, it still says the wrong thing.
    As for vol of revolution I have been able to do this.
    ∏ ∫ (f(x))^2 dx
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  6. #6
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    Re: Vol of revolution: Integral of tan(x)

    but the volume formula says ∏ ∫ (f(x))^2 dx.giving ∏ ∫ (tan(x))^2 dx.does that equate to ∏ ∫ (sin(x))^2/ (cos(x))^2 dx and integrate from there????
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  7. #7
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    Re: Vol of revolution: Integral of tan(x)

    tan^2(x)=sec^2(x)-1 So integral of tan^2(x)=tanx-x
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