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Math Help - Integrales

  1. #1
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    Integrales

    Hello Guys,

    I don't know how to solve this:



    t/ (racine) 1 + t^2 ==> for this i did this: ?



    Thanks
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  2. #2
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    are you not fimmilar with inegrals in the form of \int f(x)f'(x) dx ?

    use should know and be able to easily prove that \int f(x)f'(x) dx= \frac{1}{2} (f(x))^2

    Can you apply this to your integral ?
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  3. #3
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    Quote Originally Posted by bobak View Post
    are you not fimmilar with inegrals in the form of \int f(x)f'(x) dx ?

    use should know and be able to easily prove that \int f(x)f'(x) dx= \frac{1}{2} (f(x))^2

    Can you apply this to your integral ?
    ah so , Lnx/x = 1/2 Lnx?
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  4. #4
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    Quote Originally Posted by iceman1 View Post
    ah so , Lnx/x = 1/2 Lnx?
    please be careful with your notation, what you wrote makes no sense.

    I am sure you meant to write.

    \int \frac { \ln x}{x} dx= \frac{1}{2} (\ln x)^2 + C
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  5. #5
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    Quote Originally Posted by bobak View Post
    please be careful with your notation, what you wrote makes no sense.

    I am sure you meant to write.

    \int \frac { \ln x}{x} dx= \frac{1}{2} (\ln x)^2 + C
    Yeah sorry but i don't know how to write a mathematics letters

    so


    ==> this (integrale) 1/2 Ln (x)^2
    ==> 1/2 [Ln(1)^1 -Ln(x)^e)]
    right?
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  6. #6
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    you did not substitute the limits in the correct order. and you also confused
    <br /> <br />
\int \frac { \ln x}{x} dx= \frac{1}{2} (\ln x)^2 + C<br />
for <br /> <br />
\int \frac { \ln x}{x} dx= \frac{1}{2} (\ln x)^x + C<br />

    also you should know that \ln 1 = 0 and \ln e = 1
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  7. #7
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    Quote Originally Posted by bobak View Post
    you did not substitute the limits in the correct order. and you also confused
    <br /> <br />
\int \frac { \ln x}{x} dx= \frac{1}{2} (\ln x)^2 + C<br />
for <br /> <br />
\int \frac { \ln x}{x} dx= \frac{1}{2} (\ln x)^x + C<br />

    also you should know that \ln 1 = 0 and \ln e = 1
    yay so the final results is 1/2 right?

    what abt the other one?
    i move it and change the puissance signe like this:
    with integral from sure

    sorry abt my bad english
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  8. #8
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    yeah the answer is 1/2.

    for the next one you should recognise that you have something in the form of

    \int kf'(x)[f(x)]^n dx = k \frac {[f(x)]^{n+1}}{n+1} can you finish it off ?
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  9. #9
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    Quote Originally Posted by bobak View Post
    yeah the answer is 1/2.

    for the next one you should recognise that you have something in the form of

    \int kf'(x)[f(x)]^n dx = k \frac {[f(x)]^{n+1}}{n+1} can you finish it off ?
    ok i'll try:
    2[t (1 + t^2)]^+1/2 divided by (1/2) (with integrales)

    right?
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  10. #10
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    almost check you got the value of the constant correct and differentiate to result to check your answer.
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  11. #11
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    Using many formulae for these problems, it's an incredibly bad idea.

    These are routine problems, so we don't need formulae to make this work.

    Quote Originally Posted by iceman1 View Post
    Substitute u^2=1+t^2.

    (Correct english forms for \sqrt{~~} and \int are square root and integral.)
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  12. #12
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    Quote Originally Posted by Krizalid View Post
    Using many formulae for these problems, it's an incredibly bad idea.

    it not about using a formula, it more about identifying a standard form.
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  13. #13
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    ok Thanks Guys

    i have another thing:

    f(x)= e^(-x) (+x) -1

    Limit(+infinity)e^(-x) (+x) -1 = + infinity
    Limit(-infinity)e^(-x) (+x) -1 = + infinity

    right?
    Last edited by iceman1; February 3rd 2008 at 10:35 AM.
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