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Thread: I have an area between given curve and x axis please help .

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    I have an area between given curve and x axis please help .

    Given f is an even function and that


    $$\int_{0}^{5} f(x) dx = 12 $$

    determine

    $$\int_{-5}^{5} f(x) dx $$

    and

    Given f is an odd function and that


    $$\int_{0}^{9} f(x) dx = 4 $$



    determine

    $$\int_{-9}^{9} f(x) dx $$


    hmmm I simply double for even functions and with odd functions the areas negate each other right? making it 0 ...Is it right to assume that alot of sin and cos graphs will most likely be odd over one complete cycle?
    any help would be appreciated ...thanks.
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    Re: I have an area between given curve and x axis please help .

    if $f(x)$ is an even function ...

    $\displaystyle \int_{-a}^a f(x) \, dx = 2\int_0^a f(x) \, dx$

    if $g(x)$ is an odd function ...

    $\displaystyle \int_{-a}^a g(x) \, dx = 0$

    now the big question ... do you recall how to determine if a function is even, odd, or neither?
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    Re: I have an area between given curve and x axis please help .

    Thanks skeeter,
    I think even functions have -(fx) = (fx)
    odd -(fx) =(-fx)
    and neither doesn't suit those rules ...to do with powers and constants ..a good recap though got me thinking about it...thanks again ...makes things more clearer
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    Re: I have an area between given curve and x axis please help .

    Quote Originally Posted by bee77 View Post
    Thanks skeeter,
    I think even functions have -(fx) = (fx)
    odd -(fx) =(-fx)
    If $(\forall x)[f(-x)=f(x)]$ then $f$ is an even function.
    If $(\forall x)[f(-x)=-f(x)]$ then $f$ is an odd function.

    One of the most important even functions is the cosine function.
    One of the most important odd functions is the sine function.
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