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OpenStudy (anonymous):

Prove that the function is a constant on the interval (0, INFINITY) F(x)= integral(2x,x) 1/t dt Pls tell me what I have to do here to prove

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OpenStudy (amistre64):

the derivative of a constant is what?

OpenStudy (anonymous):

zero

OpenStudy (amistre64):

then if the derivative if F(x) = 0, then F(x) must be a constant

OpenStudy (amistre64):

its pretty simple to integrate 1/t; but there is a pretty neat rule to avoid that route

OpenStudy (amistre64):

\[\Large F(x)=\int_{a(x)}^{b(x)}f(t)~dt\] \[\Large F(x)=F[b(x)]-F[a(x)]\] \[\Large \frac{d}{dx}F(x)=\frac{d}{dx}F[b(x)]-\frac{d}{dx}F[a(x)]\] \[\Large \frac{d}{dx}F(x)=f[b(x)]~b'-f[a(x)]~a'\]

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OpenStudy (amistre64):

might have to do some limits for improper integrals to finish the proof for the interval x=0 to inf

OpenStudy (anonymous):

ok i'll try

OpenStudy (amistre64):

good luck ;)

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