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Urgent: Intergration - continous variable (probability distribution) Watch

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    Hi guys ,

    I am new to intergals here so i need your help please!


    Question: X is the delay, in hours , of a flight from Kuching , where

    f(x) = 0.2 -0.02x , 0 ≤ x ≤ 10

    a) the probability that the delay will be less than four hours

    method: using intergration:

    P(0 ≤X ≤4) = ∫04 (0.2 - 0.02x) dx
    = (0.2x-0.01x^2)0
    4
    =0.8- 0.16
    = 0.64

    Problem: i dont get why the second step in the method section! why do we have to change to 0.2x? and why 0.01?

    PLease help ! test tomorrow!

    explain . the more the better!
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    (Original post by lingwin1993)

    Problem: i dont get why the second step in the method section! why do we have to change to 0.2x? and why 0.01?

    PLease help ! test tomorrow!

    explain . the more the better! [/I]

    This is the most basic integration, and I am surprised you've not covered it.

    For a definite integral:

    For a constant:

    \displaystyle\int_b^c a = \left[ax\right]^c_b

    For a power of x other than -1:

    \displaystyle\int_b^c ax^n = \left[\frac{a}{n+1}x^{n+1}\right]^c_b
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    (Original post by lingwin1993)
    Hi guys ,

    I am new to intergals here so i need your help please!


    Question: X is the delay, in hours , of a flight from Kuching , where

    f(x) = 0.2 -0.02x , 0 ≤ x ≤ 10

    a) the probability that the delay will be less than four hours

    method: using intergration:

    P(0 ≤X ≤4) = ∫04 (0.2 - 0.02x) dx
    = (0.2x-0.01x^2)0
    4
    =0.8- 0.16
    = 0.64

    Problem: i dont get why the second step in the method section! why do we have to change to 0.2x? and why 0.01?

    PLease help ! test tomorrow!

    explain . the more the better!
    Note the advice you've already been given, but you need to cover integration fast, otherwise you'll be stuck if a similar question comes up!
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    (Original post by davros)
    Note the advice you've already been given, but you need to cover integration fast, otherwise you'll be stuck if a similar question comes up!
    i tried reading up but i am having a hard time understanding it. Do you have like a website which you can sent me now so that i can question you anything i dont understand now ?
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    (Original post by ghostwalker)
    This is the most basic integration, and I am surprised you've not covered it.

    For a definite integral:

    For a constant:

    \displaystyle\int_b^c a = \left[ax\right]^c_b

    For a power of x other than -1:

    \displaystyle\int_b^c ax^n = \left[\frac{a}{n+1}x^{n+1}\right]^c_b

    Do you mind telling me what does each symbol stand for so that i can understand the formula better please?
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    (Original post by lingwin1993)
    i tried reading up but i am having a hard time understanding it. Do you have like a website which you can sent me now so that i can question you anything i dont understand now ?
    In a single sentence, integration is the reverse process to differentiation.

    How much differentiation have you covered?
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    (Original post by lingwin1993)
    Do you mind telling me what does each symbol stand for so that i can understand the formula better please?
    a,b,c,n, are just constants. you can substitute in their real values when integrating an actual function.

    How is it you've not covered basic integration?
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    (Original post by davros)
    In a single sentence, integration is the reverse process to differentiation.

    How much differentiation have you covered?
    i was not thought about differentiation but i know that differentiation is a measure of the rate the slope changes?

    so.. it would be great if like i can understnd integration with your help
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    (Original post by ghostwalker)
    a,b,c,n, are just constants. you can substitute in their real values when integrating an actual function.

    How is it you've not covered basic integration?

    Because took foundation maths for GCSEs and i have not learnt these kind of stuff and now that i am taking statistics in Uni. i have to learn these. anyway you can help me now?
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    To integrate, just add one to the power and divide by the new power.
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    (Original post by SecretDuck)
    To integrate, just add one to the power and divide by the new power.
    example please?
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    (Original post by lingwin1993)
    i was not thought about differentiation but i know that differentiation is a measure of the rate the slope changes?

    so.. it would be great if like i can understnd integration with your help

    (Original post by lingwin1993)
    Because took foundation maths for GCSEs and i have not learnt these kind of stuff and now that i am taking statistics in Uni. i have to learn these. anyway you can help me now?
    No offence, but people normally spend a couple of terms or more getting to grips with differentiation and integration as part of A level - it's not the sort of thing you can breeze through in an evening.

    Did your course not have prerequisites before you joined? Are your course tutors aware that you haven't covered topics from calculus that they are assuming as part of the stats course?
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    (Original post by davros)
    No offence, but people normally spend a couple of terms or more getting to grips with differentiation and integration as part of A level - it's not the sort of thing you can breeze through in an evening.

    Did your course not have prerequisites before you joined? Are your course tutors aware that you haven't covered topics from calculus that they are assuming as part of the stats course?
    They are aware - the lecturers. i just need to brush up my skills but understanding comes first. .its ok , i can try my best ..
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    (Original post by SecretDuck)
    To integrate, just add one to the power and divide by the new power.
    This works until you get a non-polynomial. A more versatile one-liner:
    Think what would, when differentiated, give you the given function.
    The Fundamental Theorem of Calculus states that \int_a^bf'(x)=f(b)-f(a); this is the single most important point of "how to integrate". Then there are a couple of rules: integration by parts (which is what you get when you integrate the product rule for differentiation):
    \frac{d}{dx}(f g) = f \frac{d}{dx}g + g \frac{d}{dx} f, so f g = \int f \frac{d}{dx}g dx + \int g \frac{d}{dx} f dx.
    Also the analogue to the chain rule:
    \int f'(x) f(x)^n dx = \int \frac{f(x)^{n+1}}{n+1} dx.
    If you don't know what the chain rule and product rule etc are (that is, if you've not done differentiation), and you have an exam tomorrow, I'm afraid you should concentrate on whatever parts of the exam don't contain calculus.
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    (Original post by lingwin1993)
    example please?
    \int_a^b x^3 dx = [\frac14 x^4]_a^b = b^4-a^4
    The notation [f(x)]_a^b is shorthand for f(b)-f(a).
    Since \frac{d}{dx} (\sin(x) + C) = \cos(x), where C is an arbitrary constant, it follows that \int \cos(x) dx = sin(x) + C.
    Conventionally, we miss out the C in a "definite integral" - an integral with the a and b on the integral sign - because it vanishes anyway:
    \int_a^b x^3 dx = [\frac14 x^4+C]_a^b = b^4+C-(a^4+C) = b^4-a^4.
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    (Original post by lingwin1993)
    example please?
    Say you need to integrate 2x

    Add one to the power: 2x^2

    Divide by the new power (in this case, 2): 2x^2 / 2

    I = x^2 (+ c )
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    (Original post by Smaug123)
    This works until you get a non-polynomial. A more versatile one-liner:
    Think what would, when differentiated, give you the given function.
    The Fundamental Theorem of Calculus states that \int_a^bf'(x)=f(b)-f(a); this is the single most important point of "how to integrate". Then there are a couple of rules: integration by parts (which is what you get when you integrate the product rule for differentiation):
    \frac{d}{dx}(f g) = f \frac{d}{dx}g + g \frac{d}{dx} f, so f g = \int f \frac{d}{dx}g dx + \int g \frac{d}{dx} f dx.
    Also the analogue to the chain rule:
    \int f'(x) f(x)^n dx = \int \frac{f(x)^{n+1}}{n+1} dx.
    If you don't know what the chain rule and product rule etc are (that is, if you've not done differentiation), and you have an exam tomorrow, I'm afraid you should concentrate on whatever parts of the exam don't contain calculus.
    I of course meant the basic integration in the OP. For trig, hyperbolic trig and other complex functions, new rules are needed.

    I just don't want to confuse the OP by talking about substitution or parts.
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    (Original post by SecretDuck)
    I of course meant the basic integration in the OP. For trig, hyperbolic trig and other complex functions, new rules are needed.

    I just don't want to confuse the OP by talking about substitution or parts.
    Ah :P I went the "crash course" route - OP, feel free to ignore my post if you aren't going to invest serious time and effort into calculus tonight (it takes some work to understand, the first time you see it.)
 
 
 
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