## anonymous one year ago 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, +∞)

1. anonymous

this is the function

2. anonymous

not really sure where to start on this one

3. Empty

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.

4. anonymous

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

5. anonymous

no wait that cant be right

6. anonymous

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

7. anonymous

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

8. anonymous

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?

9. Empty

Yeah perfect!

10. anonymous

YAY!!

11. Empty

Well not quite because zero is a constant slight note

12. anonymous

thanks man !

13. Empty

zero is the derivative of a constant!

14. anonymous

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

15. Empty

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

16. anonymous

boom indeed

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