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Thread: HSC 2018 MX2 Integration Marathon

  1. #26
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    Re: HSC 2018 MX2 Integration Marathon

    only requires u substitution.
    Last edited by mrbunton; 2 Apr 2018 at 12:08 PM.

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    Traveller from the North fan96's Avatar
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    Re: HSC 2018 MX2 Integration Marathon





    Justifying this substitution:

    has a solution for only when and .

    The domain of the integrand is and .

    does not exist only when . But since this range is undefined in the integrand to begin with, the substitution is valid.

    So,



    Substituting, we get



    Not sure if that second last step was valid though.

    (edit: oops forgot to sub back in)

    And so



    and by considering the appropriate right angled triangle, . Since that's always positive, the sign function on the left can be eliminated.

    So we have

    Last edited by fan96; 3 Apr 2018 at 6:54 PM.
    HSC 2018 - [English Adv.] • [Maths Ext. 1] • [Maths Ext. 2] • [Chemistry] • [Software Design and Development]

    1(3√3) t2 dt cos(3π/9) = log(3√e) | Integral t2 dt, From 1 to the cube root of 3. Times the cosine, of three pi over nine, Equals log of the cube root of e.

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    Re: HSC 2018 MX2 Integration Marathon

    an easier way is to just use the substitution u = sqrt(x)
    the integrand will be 2/sqrt(u^2+1), which is trivial to integrate (those usual log ones)
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    Re: HSC 2018 MX2 Integration Marathon

    correct but the two tan signs are generally said to cancel each other out; although i understand it can vary from +-1. that being said if u look at example at the integral tanx/|tanx| it is a horizontal line being split up into positive and negative in pi/2 segments at a time and hence u should not be allowed to take it out theoretically (although area stays the same; definite integral get affected from my understanding)but discontinuous graphs in integration are probably beyond the scope of even ext2(when dealing with indefinite integrals btw; or i havent been taught it yet). Its easier just to cancel the tan out imo at this level.

    im not completely sure but in the solution i got had the tan cancelled out
    Last edited by mrbunton; 4 Apr 2018 at 9:30 PM.

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    Re: HSC 2018 MX2 Integration Marathon

    is anyone else seeing a bunch of extra addition symbols lodged between every character or is that just me
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by jathu123 View Post
    an easier way is to just use the substitution u = sqrt(x)
    the integrand will be 2/sqrt(u^2+1), which is trivial to integrate (those usual log ones)
    may as well just jump ahead and multiply by
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

  7. #32
    Junior Member supR's Avatar
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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by Paradoxica View Post
    is anyone else seeing a bunch of extra addition symbols lodged between every character or is that just me
    Yeah I'm seeing that and it's really confusing


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    Re: HSC 2018 MX2 Integration Marathon

    How to do this question https://imgur.com/a/jrRra

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    Re: HSC 2018 MX2 Integration Marathon

    is it 13/15 pi u^2 ??

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    Traveller from the North fan96's Avatar
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    Re: HSC 2018 MX2 Integration Marathon

    Quote Originally Posted by CapitalSwine View Post
    How to do this question https://imgur.com/a/jrRra
    We can get the volume of the solid by taking the volume of from 0 to 1 (rotated about the y-axis) and then subtracting the volume of the cylinder inside, which has radius and height 1.

    Last edited by fan96; 12 Apr 2018 at 7:44 PM.
    CapitalSwine likes this.
    HSC 2018 - [English Adv.] • [Maths Ext. 1] • [Maths Ext. 2] • [Chemistry] • [Software Design and Development]

    1(3√3) t2 dt cos(3π/9) = log(3√e) | Integral t2 dt, From 1 to the cube root of 3. Times the cosine, of three pi over nine, Equals log of the cube root of e.

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