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c2 integration watch

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    im doing c2 integration homework atm, and while i know what to do and can get the marks, i really have no idea what im doing and why. i've been told im finding the area under a curve when using definite integrals, but how am i doing it? whats happening? and wtf is an integral, anyway? :confused: or a derivative for that matter?

    can anyone explain any of that in laymans terms please?
    thanks anyone
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    What you are pretty much doing with integration is that you are finding the area under the curve between two limits. This could be visualized by a perfect form of an implementation of the trapezium rule, where h is an infinitessimally small number and there are an infinite amount of trapeziums of which their area is calculated. It's a terrible way to explain it but that's the only way I can in 'laymen's terms'.

    A deriative is just a gradient function for any point within the equation of which its derive. That is, for any value of x, the gradient at that very point can be calculated by putting the value of x into the derived gradient function.
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    (Original post by innerhollow)
    And 10 is your final answer. PM me if you need any more help, but please look over your textbook because you need to learn how to do stuff like this.
    Thanks, i have learnt what to do, like i know how to answer the questions and get the marks, what im trying to figure out is why the method we use works.

    from serrated_colon's description "This could be visualized by a perfect form of an implementation of the trapezium rule, where h is an infinitessimally small number and there are an infinite amount of trapeziums of which their area is calculated."
    firstly, i wish to know how 1/2h[(y0+yn)+2(...yn-1)]
    means ax^n+1/n+1 gives me the area?
    i just think im going to understand it better and be able to adapt it better to wierdly phrased exam q.s etc if i understand what is actually happening, rather than just blindly accepting the method im told

    thanks for the reply and any further ones

    p.s. i dont really know how to use this latex thing so it may look a bit retarded
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    Agreed, in the textbooks it explicitly says that the proofs for these things are beyond the level you need to know. I don't think that the 'weirdly asked questions' will require any of the principles involved in proving these results though, the worst they can ask is 'estimate the area under the curve 1/x between limits a and b' with regards to the trapezium rule. Differentiation is a different issue though, you have to understand the problem solving aspect with regards to local maxima/minima. It's not too difficult for c2 though.
 
 
 
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Updated: February 13, 2010

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