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Higher Maths (P1) Question 8(c)

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    #32
    Yuugib
    Registered Users Posts: 432 ✭✭Yuugib


    61/6 the second time i v done it


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    #33
    raah!
    Registered Users Posts: 2,629 ✭✭✭raah!


    Does anyone know if it's acceptable to integrate between the graph and the y axis to get the scond part? or are you only able to do that with sidewaysy graphs?


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    #34
    looly
    Closed Accounts Posts: 16 ✭looly


    Ah crap....i got 44/5........ah well! i think i did a few bits right so il get my attempt marks anyway lol


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    #35
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,849 Mod ✭✭✭✭Michael Collins


    The correct answer is 32/3. The method is quite simple (but might take a while to see how it works):

    Area = Int(4 -x^2 - (1 - 2x))dx from -1 up to 3

    = 32/3 square units (or 10 and 2/3)


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    #36
    tramoredude
    Closed Accounts Posts: 122 ✭✭tramoredude


    Michael Collins wrote: »
    The correct answer is 32/3. The method is quite simple (but might take a while to see how it works):

    Area = Int(4 -x^2 - (1 - 2x))dx from -1 up to 3

    = 32/3 square units (or 10 and 2/3)


    It can't be that easy! :D

    Will you explain it fully please? Its killing me inside!


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    #37
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,849 Mod ✭✭✭✭Michael Collins


    tramoredude wrote: »
    It can't be that easy! :D

    I'm afraid it looks like it is :)
    tramoredude wrote: »
    Will you explain it fully please?

    It's not the easiest to explain without diagrams but qualitatively you're looking for the area between the curve and the line. If you subtract the height of the line from the height curve, you've now got a new curve, the area between it and the x-axis is what you're looking for - hence just a simple integration between the limits.
    tramoredude wrote: »
    Its killing me inside!

    That's why I'm not a big fan of exam post-mortems, just concentrate on the next exam, that's the most important one now...


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    #38
    yenoolnairb
    Closed Accounts Posts: 6 ✭yenoolnairb


    I didn't know what to do cos the area went under the x axis and behind the y axis. Integration gets the area between what you're integrating and the x axis (yes?) so wouldn't get the underneath bit i figured so i shifted the whole thing into the positive quadrant by changing xs to x+1s and ys to y+5s and then just integrated between 4 and 0. how does that sound? is it allowed?


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    #39
    ~Candy~
    Closed Accounts Posts: 435 ✭✭~Candy~


    Davidius wrote: »
    That question looks big and scary to my poor 5th year brain. D:

    haha!! yea.


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    #40
    ~Candy~
    Closed Accounts Posts: 435 ✭✭~Candy~


    i think i got the bit under the curve above the x-axis sumthing lyk , -1 to 3
    and minus the triangle and i added the the bit under the curve

    lol xpt i kinda points...i got sumthing over 3..
    so wrong tho, i hope i cud get sum att. marks..

    how do ye do b part 2 like !!


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    #41
    Timans
    Registered Users Posts: 2,370 ✭✭✭Timans


    I got 32/3 as well.

    But, I did mine really wrong. I hope I'll get 15/20 for it though.


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    #42
    shanedownfall
    Registered Users Posts: 81 ✭✭shanedownfall


    I'm pretty sure i got 61/6 for this question. Which doesn't seem to be right... But with a lot of people getting it i presume it's due to a small error...

    What i did, and i'm really not sure if it's a correct method; is integrate from the y axis to find the area underneath the x-axis. I isolated x, getting (4-y)^1/2, and integrated this using 0 and -5 as limits. I then took away the area of the triangle, and small rectangle that were also accounted for in the integration part.

    Does that seem right?... The Part over the x-axis was just basic integration. And i'm sure most will pick up a lot of marks for getting it right. ;)


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    #43
    Challenged
    Closed Accounts Posts: 40 ✭Challenged


    I just found the solution to Q. 8

    http://studentxpress.ie/papers/intsoln2008.pdf


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    #44
    LCFin.yay
    Closed Accounts Posts: 35 ✭LCFin.yay


    ye know that the marking schemes are posting on www.examinations.ie soon after the exams over yeah? lol


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    #45
    devinejay
    Registered Users Posts: 639 ✭✭✭devinejay


    32/3, and so did a friend who I trust (Read;she's a maths nerd)


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    #46
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,849 Mod ✭✭✭✭Michael Collins


    Challenged wrote: »
    I just found the solution to Q. 8

    http://studentxpress.ie/papers/intsoln2008.pdf

    Nicely presented solution there. The solution is a bit longer than necessary, however.
    LCFin.yay wrote: »
    ye know that the marking schemes are posting on www.examinations.ie soon after the exams over yeah? lol

    They won't be up until after the results are out, as the marking scheme is decided only after the papers are corrected.


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    #47
    Mr. Blah
    Registered Users Posts: 43 ✭Mr. Blah


    I did what the solution shows (with the dividing it up and then adding it at the end) but I got 13. Must of made a slip up somewhere. Least I'll get most marks I suppose :P


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    #48
    Timans
    Registered Users Posts: 2,370 ✭✭✭Timans


    I got the right answer but didn't do it the right way.

    How many marks are going for the answer?


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    #49
    less is more
    Closed Accounts Posts: 17 ✭less is more


    Ok so the general consensus is 32/3.

    So unfortunately for me, my nice whole 19 units^2 was WRONG. Thanks guys for raining on my parade lol. I really thought my whole number answer was right... ah well I've never got an integration-area question right before, so why break tradition for the exam? Now onto paper two...


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    #50
    MathsManiac
    Registered Users Posts: 1,595 ✭✭✭MathsManiac


    Why is nobody listening to Michael Collins' words of wisdom? Are you all Dev fans or something?

    Surely everyone knows by now, (since it was pointed out in another thread before the exam,) that if f(x) lies above g(x) between x=a and x=b, then, no matter where the axes lie, the area between them is the integral from a to b of [f(x)-g(x)] dx.

    So yes, it is as easy as MC said.


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    #51
    starkinter
    Closed Accounts Posts: 59 ✭✭starkinter


    Unfortunately, this method isn't how most people were taught to approach questions.

    Looking at it now, it does make lots of sense.


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    #52
    CaramelBear
    Closed Accounts Posts: 70 ✭✭CaramelBear


    32/3 is what I got!! Oh me, oh my. I hope it's right! It seems to be. It has to be.

    -prays fervently-


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