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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, +∞)

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  1. anonymous
    • one year ago
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    this is the function

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  2. anonymous
    • one year ago
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    not really sure where to start on this one

  3. Empty
    • one year ago
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    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
    • one year ago
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    okay so then \[\frac{ 1 }{ 4x} - 1/x\]

  5. anonymous
    • one year ago
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    no wait that cant be right

  6. anonymous
    • one year ago
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    \[((\frac{ 1 }{ 4x })(4)) - (\frac{ 1 }{ x })\]

  7. anonymous
    • one year ago
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    \[ \frac{ 4 }{ 4x} - \frac{ 1 }{ x }\]

  8. anonymous
    • one year ago
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    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
    • one year ago
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    Yeah perfect!

  10. anonymous
    • one year ago
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    YAY!!

  11. Empty
    • one year ago
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    Well not quite because zero is a constant slight note

  12. anonymous
    • one year ago
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    thanks man !

  13. Empty
    • one year ago
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    zero is the derivative of a constant!

  14. anonymous
    • one year ago
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    okay that makes sense , yea ... ZERO IS THE DERIVATIVE OF A CONSTANT !!

  15. Empty
    • one year ago
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    Haha yeah so you got zero for your derivative, booooom done! :P

  16. anonymous
    • one year ago
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    boom indeed

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