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C4 Formula for calculating area under a curve

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    ∫y dx/dt

    When attempting to calculate the area under a curve. Do you always use the above formula? Or are there exceptions? Because I am sure I learnt a different formula in C2, just can't remember

    Thanks
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    Most often you will need \int y dx
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    Not sure if I've grasped what you're asking...
    You use the equation of the curve you are integrating. It depends if the equation is y=3x^2 or y=3t^2 as to whether you use dx or dt.
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    (Original post by BabyMaths)
    Most often you will need \int y dx
    HOw do you know whether to apply the above formula, or the one I gave? Thanks
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    (Original post by sabre2th1)
    HOw do you know whether to apply the above formula, or the one I gave? Thanks
    I think you meant \int y \frac{dx}{dt}dt. This is handy when you have parametric equations.
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    Given a function f(x), the notation:

    \displaystyle A = \int_b^c f(x)\ \text{d}x

    Is more or less equivalent to saying: "A is equal to the sum of the values of f(x) over all values of x between b and c"

    In other words, A is the area under the curve y = f(x) between the values x = b and x = c.

    (EDIT: assuming the curve does not cross the x-axis.)
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    (Original post by james.h)

    Is equivalent to saying: "A is equal to the sum of the values of f(x) over all values of x between b and c"
    Kind of a dodgy definition don't you think?
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    (Original post by BabyMaths)
    Kind of a dodgy definition don't you think?
    Implicitly assumed here are that the "function" is "nice" (continuous, piecewise finite, &c). :ninja:

    ...Okay, fine, but it gets the general idea across.

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Updated: June 20, 2012
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