Question

definite integral! help please

Answer 1

\[\int\limits_{ e}^{e^2}lnx/2x\]

Answer 2

\[\int\limits_{e^2}^{e} \frac{ lnx}{ 2x }dx\]

Answer 3

Rewrite it first and then figure out a appropriate substitution:

\[\Large \frac{1}{2}\int \ln x \cdot \frac{1}{x} dx \]

Answer 4

at this point, something should jump into your eyes.

Answer 5

this is a definite integral, though

Answer 6

do you use the fundamental theorem of calculus?

Answer 7

Well I dropped the limits, no matter if it's a definite integral or not, you always need to first integrate it. As soon as you have that Function, you can plugin the limits and evaluate. But you're right, that is the fundamental theorem of Calculus

Answer 8

after you do what spacelimbus said to do, you separate the integral into 2 parts one from 0 to e and 0 to e^2 and say \[\int\limits_{0}^{e^2}-\int\limits_{1}^{e}\]

Answer 9

whoops, that should say 0 to e not 1

Answer 10

Always double check the limits, 0 is rather delicate here, the function isn't defined at x=0

Answer 11

(I usually miss that part, so I write that down as a reminder for myself)

Answer 12

what do you need help with? Finding the anti-derivative, or what a definite integral is?

Answer 13

solving definite integrals..in general

Answer 14

where did the 0 come from in \[\int\limits_{0}^{e^2}\]

Answer 15

fine you can start it at 1 instead, it shouldnt really matter what the lower bound is as long as you use the same lower bound for both integrals iirc