another problem i'm having trouble with

Show that the function F of x equals the integral from x to 4 times x of 1 over t dt is constant on the interval (0, +∞)

Question

another problem i'm having trouble with 

Show that the function  F of x equals the integral from x to 4 times x of 1 over t dt is constant on the interval (0, +∞)

anonymous · Answer

this is the function

anonymous · Answer

not really sure where to start on this one

empty · Answer

Hmmm well maybe you could take its derivative, and since the derivative of a constant is 0, if its derivative is 0 then you know it was a constant.

anonymous · Answer

okay so then $$\frac{ 1 }{ 4x} - 1/x$$

anonymous · Answer

no wait that cant be right

anonymous · Answer

$$((\frac{ 1 }{ 4x })(4)) - (\frac{ 1 }{ x })$$

anonymous · Answer

$$ \frac{ 4 }{ 4x} - \frac{ 1 }{ x }$$

anonymous · Answer

the 4 cancel out and we end up with zero , and zero is a constant thus the function is constant .... does that seem right to you?

empty · Answer

Yeah perfect!

anonymous · Answer

YAY!!

empty · Answer

Well not quite because zero is a constant slight note

anonymous · Answer

thanks man !

empty · Answer

zero is the derivative of a constant!

anonymous · Answer

okay that makes sense , yea ... ZERO IS THE DERIVATIVE OF A CONSTANT !!

empty · Answer

Haha yeah so you got zero for your derivative, booooom done! :P

anonymous · Answer

boom indeed