Question

can someone help me to this integral

Answer 1

\[\int\limits_{\pi/2}^{\pi} 2\cot \theta/3\]

Answer 2

its suppose t be pi/2 on the lower limit

Answer 3

pull out 2/3 out of that integral

Answer 4

I got as far as : \[6\ln \left| sinu \right|\]

Answer 5

and i am not sure if that is even right

Answer 6

use U sub

Answer 7

yeah ; \[\int\limits_{}^{} \cot u =\ln \left| \sin u \right|\]

Answer 8

\[\int \frac{\text{Cos}[x]}{\text{Sin}[x]}\text{dx}\]
\[\int \frac{1}{u}\text{du}\]
\[\ln [u]=\ln [\text{Sin}[x]]\]

Answer 9

So you are right

Answer 10

yeah but i need some help doing it cause i am getting lost

Answer 11

??

Answer 12

problem is this is an indefinite integral because cot is not defined at
\[\pi\]

Answer 13

the books gives me an answer if : ln27

Answer 14

you found an antiderivative, but you cannot plug in
\[\pi\] because you will get
\[\ln(0)\] which is undefined

Answer 15

hold the phone

Answer 16

ooooooooh

Answer 17

anti derivative is
\[6\ln(\sin(\frac{x}{3}))\] yes

Answer 18

put x =
\[\pi\] get
\[\ln\sin(\frac{\pi}{3})=\ln(\frac{\sqrt{3}}{2})\]

Answer 19

plug in
\[\frac{\pi}{2}\] get
\[\ln(\frac{1}{2})\]

Answer 20

now
\[\ln(\frac{\sqrt{3}}{2})-\ln(\frac{1}{2})=\ln(\sqrt{3})\]

Answer 21

my that property of logs that says divisions become subtractions

Answer 22

so you have
\[\ln(\sqrt{3})=\ln(\sqrt{3}^6)\] gives your solution manual answer

Answer 23

sorry that last line was a typo. it should say
\[6\ln(\sqrt{3})=\ln(\sqrt{3}^6)\]

Answer 24

which is in fact
\[\ln(27)\]

Answer 25

capice?

Answer 26

oh, what a dummy i am

Answer 27

thanks,

Answer 28

just properties of hte logs at play. yw