Thread: Basic Integration

Find the area between y=ln(x) and the x axis on the interval [1,e^2]

I know how to integration, but is this possible? How would I integrate lnx?

Originally Posted by Sm10389

Find the area between y=ln(x) and the x axis on the interval [1,e^2]

I know how to integration, but is this possible? How would I integrate lnx?

one way, the most famous, is to integrate by parts. using u = ln(x) as the function you differentiate and dv = dx as the function you integrate

ln(x) has actually been integrated several ways on this forum, it might do you good to do a quick search

Ok so use 1 and lnx.

My answer is xlnx-1

is that right?

Originally Posted by Sm10389

Ok so use 1 and lnx.

My answer is xlnx-1

is that right?

no

maybe i just wrote it wrong

u=ln(x)
v'=1
u'=1/x
v= x

=
lnx*x - x(1/x)
=
(lnx) - 1

Where is it wrong

Originally Posted by Sm10389

maybe i just wrote it wrong

u=ln(x)
v'=1
u'=1/x
v= x

=
lnx*x - x(1/x)
=
(lnx) - 1

Where is it wrong

you have to integrate the second term according to the formula...

that is integrating... by parts.