Question

Determine if the integral converges or not and show steps : integral 1 to pi/2 tan(x) dx

Answer 1

I really need help

Answer 2

find the antiderivative of tan(x) first

Answer 3

which is?

Answer 4

(solve the integral without plugging limits first)

Answer 5

can you work the thing out for me?

Answer 6

tan(x) = sin(x)/cos(x)
let cos(x) = u
then du = -sin(x)dx
so
tan(x)dx = -du/u
right ?

Answer 7

yes ok continue

Answer 8

so now integral of (-du/u) is simply -ln(u) = -ln(cos(x))

Answer 9

agree ?

Answer 10

so far yes now what

Answer 11

it is in fact -ln|cos(x)|

Answer 12

yes ok

Answer 13

now we have to plug limits but doing so carefully .. by carefully i mean taking the limits

Answer 14

ok so how

Answer 15

as you can see lim [-ln|cos(x)| ] as x-> pi/2 is not converges right ?

Answer 16

yes i see

Answer 17

its divergent but at what number?

Answer 18

then the whole integral wont converge

Answer 19

so whats our final conclusion?

Answer 20

not converges

Answer 21

at what number? no number?

Answer 22

give up.

Answer 23

You cannot DIVERGE at a number - \[ \Huge \color{green} {\text{You can only diverge to infimity}} \pm \]

Answer 24

I like this \[ \color{#F87431}{\Huge Expressionism\text{ of COLOR}}\]

Answer 25

IT drains out the unneeded fatigue ....

Answer 26

ITT: we Devolve to Inanity

Answer 27

Did you know that the measure of finitely provable theorems in all true theorem is very LOW

Answer 28

this integral diverges to 42/(6*7); equivalent to answer/(question)

Answer 29

Read Godel and Church

Answer 30

Madam ! My name is Church! Alonzo Church, but you can call me Alonzo...
http://en.wikipedia.org/wiki/Alonzo_Church

Answer 31

But this guy is the MOST INSPIRING and soul elevating of all Logicians
http://en.wikipedia.org/wiki/Raymond_Smullyan \[ \LARGE \text{"The LAdy and the Tiger" by Raymond Smullyan}\]

Answer 32

Elvis has left the building