logarithmic and exponential functions - area help (1 Viewer)

[kaha167]

find the area between: y = ln x, y = 2 and y = 4. the answer is 47.2 units^2.
I can get nowhere near this number..
can anyone possible help me?
Greatly appreciated.

 

[cutemouse]

find the area between: y = ln x, y = 2 and y = 4. the answer is 47.2 units^2.
I can get nowhere near this number..
can anyone possible help me?
Greatly appreciated.

I'll assume that you mean the area between y=2, y=4, the curve and the y axis...

y=lnx
e^y=x

Required area =
units^2

 

[hscishard]

find the area between: y = ln x, y = 2 and y = 4. the answer is 47.2 units^2.
I can get nowhere near this number..
can anyone possible help me?
Greatly appreciated.

One way of doing is noticing that y= Inx is a slanted version of y=e^x. Inverse or something like that.
Intergrating e^y is e^y
Then solve the definite integral using the bounds 4 and 2

 

[hscishard]

I'll assume that you mean the area between y=2, y=4, the curve and the y axis...

y=lnx
e^y=x

Required area =
units^2

Ooo rearranging.

 

[kaha167]

oh ok, i didn't realise/think i could invert the log to become an e
thanks very much for your help

 

[Aquawhite]

oh ok, i didn't realise/think i could invert the log to become an e
thanks very much for your help

You can only invert it to the exponential (e) because the log is in the natural base, e, such that it is lnx. If it weren't this way (although I highly doubt you would get this), you wouldn't be able to do it.

 

[cutemouse]

You can only invert it to the exponential (e) because the log is in the natural base, e, such that it is lnx. If it weren't this way (although I highly doubt you would get this), you wouldn't be able to do it.

Or you could've done Area rectangle - integral... but that'd require knowledge of integration by parts...