Question

CONVERGENT OR DIVERGENT? This is convergent (checked on Wolf), but I am having trouble showing it:

Answer 1

\[\int\limits\limits_{\pi/2}^{\pi} 34\csc(x)dx\]

Answer 2

@EarthCitizen
@experimentX
@apoorvk
@FoolforMath
@amistre64
@Mertsj

Answer 3

\[\int\limits\limits\limits_{\pi/2}^{\pi} 34\csc(x)dx = \lim_{a \rightarrow \pi-} \int\limits\limits\limits_{\pi/2}^{a} 34\csc(x)dx\]

Answer 4

\[\int\limits\limits_{}^{}\csc(x) dx = \ln|\csc(x) - \cot(x)| + C\]
^indefinite integral of csc(x), lets get that straight..

Answer 5

singularity at pi/2
\[ \lim_{x->\pi} \ln|\csc x - \cot x| - \ln|\csc \pi/2 - \cot \pi/2|\]
Doesn't it look like \( \infty - \infty \)
try multiplying by conjugate and use L'Hospital rule

Answer 6

Not sure though ... let me check from wolfram!!

Answer 7

should be closed
http://www.wolframalpha.com/input/?i=integrate+csc%28x%29+from+pi%2F2+to+pi

Answer 8

Try to find the value of inner limit
\[ \ln \left | \lim_{x\rightarrow \pi}\frac{\csc x - \cot x}{\csc (\pi/2) - \cot (\pi/2)}\right |\]

Answer 9

Sorry that didn't work!!

Answer 10

@amistre64

Answer 11

@phi

Answer 12

@.Sam.

Answer 13

@amistre64. We have got up to the limit part, and there we are having trouble evaluating it. It HAS to be convergable. We checked on Wolf

Answer 14

convergent or divergent would imply some trouble spots that need to be addresses

Answer 15

1/sin is troublesome at sin = 0

when does sin = 0 on your interval

Answer 16

http://i1084.photobucket.com/albums/j409/QRAWarrior/MATA36/MATA36-A4-Question2.png

sin=0 for pi.

Answer 17

and i see youve already determined the integral part

ln(csc - cot) right?

Answer 18

Yes.

Answer 19

and the tricky part is the -F(a) condition eh

Answer 20

Yea! If ONLY it were the OTHER way around

Answer 21

Then I could exponentiate the ln's argument by -1.

Answer 22

\[\lim_{a\to\ pi}-\ln (\csc a - \cot a)\]

Answer 23

How???

Answer 24

Where did that -1 come from?

Answer 25

F(b) - F(a) is the solution

Answer 26

you know F(b)

Answer 27

But pi is the upper limit. How can you get the -1 in front of the ln?

Answer 28

it is? such tiny little text

Answer 29

Yes