Integrate lnx (1 Viewer)

[micuzzo]

how would i integrate ln x

 

[lolokay]

well you would need to use integration by parts (4u) or have a lead in .

if you want to try and figure it out: what's a function that you know would give you ln x, and something else, when differentiated?

 

[Trebla]

It's beyond the scope of the 2 unit syllabus...If you were to find an area with a definite integral, you would most likely convert the log into an exponential which makes it easier to integrate. Another way is to differentiate xln x and derive the integral from there:
d(xln x)/dx = 1 + ln x
xln x + c = ∫(1 + ln x) dx
xln x + c = x + ∫ ln x dx
.:∫ ln x dx = xln x - x + c

 

[arjungamer123]

Derivative of xlnx is lnx +1

Therefore, indefinite integral of lnx + 1 = xlnx
Therefore, if you split up the left side,intergrate each term at a time, you can see that 1's indefinite integral is x. Then take x to the other side.

then you have it

Also, remember + C

 

[micuzzo]

can someone try this... the find area bounded by the line y=ln x the x aixs and lines x=2 and x=4

is ther a way to do it knowing x=e^y

 

[Trebla]

If you want to use the exponential, draw a diagram and consider the rectangles...
This same question was asked before:
http://community.boredofstudies.org...195864/finding-area-underneath-log-graph.html