Question

show that integration of cosec 2x dx limit 1/6π to 1/3π = 1/2ln3

Answer 1

@tkhunny @thomaster @SithsAndGiggles @Compassionate guys anyone help me please?

Answer 2

This? \(\int\limits_{\pi/6}^{\pi/3}\;\csc^{2}(x)\;dx\;=\;\dfrac{1}{2}\ln(3)\)??

Have you considered a substitution, maybe \(u = \cot(x)\)?

Answer 3

please help me with this I'm dying trying to solve this :(

Answer 4

@phi @mathmath333 @aum @kohai help me anyone :((((((

Answer 5

I would re-write it using sin. Can you do that ?

Answer 6

\[1/\sin2x\]

Answer 7

now we need an idea.

Answer 8

I used the double angle formula and I got 1/2sinxcosx but how to proceed from there?

Answer 9

yes, I looked at that. but so far, that isn't helping.

Answer 10

yea I got stuck there :(

Answer 11

there must be a way

Answer 12

using substitution method?

Answer 13

can we substitute 2theta=x

Answer 14

why can't we just use the double angel formula and convert sin 2x into 2sinxcosx?

Answer 15

how about
\[ \frac{1}{2} \int \frac{\sin^2(x) + \cos^2(x)}{\sin(x) \cos(x)} dx \]

Answer 16

that looks doable.

Answer 17

write it as
\[ \frac{1}{2} \int \frac{\sin(x)}{\cos(x)} + \frac{\cos(x)}{\sin(x)} \ dx \]

Answer 18

YEAHHHH I got the answer already thank you very much you guys are so helpful glad I found you guys

Answer 19

Seriously, did you try \(u=\cot(2\theta)\)?