jessij04
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Show that the function f(x)= integral from x to 3x 1/t ft is constant on the interval (0, positive infinity)

Respuesta :

apologiabiology
[tex] \int\limits^{3x}_x { \frac{1}{t} } \, dt [/tex]
integrate to get
[tex][ln|t|]^{3x}_x=ln|3x|-ln|x|=ln| \frac{3x}{x}| =ln |3|=ln(3)[/tex]
this only is true when x>0
when x turns negative, we get -ln(3) because of math

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