Question

Hi there
May I know how to integrate this,
1/((x^2-9)^(1/2)). please note, this is definite integral. x is, [2*sqrt(3)] to [3*sqrt(2)]

Answer 1

This looks like a trig-sub integral. Have you sketched a reference triangle?

Answer 2

Here is a summary of the trig subs I made for my students. :)

Answer 3

=\[\int\limits_{2\sqrt{3}}^{3\sqrt{2}}1/\sqrt{x^2-9} dx\]

Answer 4

you can use online wolfram alpha

Answer 5

exactly I went to upto Integral of (sec ). But I cant work out after that step.

Answer 6

how abt replacing sqr(x^2-9) with a t?

Answer 7

Angela if you let t = sqrt ( x - 9) dt does not equal a constant, so that won't work. You need a trig sub.

Answer 8

i thought sqr(x^2-9)=t---->x=sqr(t^2+9)
dx=(sqrt^2+9)'dt=t/(sqr(t^2+9)dt...
won't work???? :S

Answer 9

http://www.wolframalpha.com/input/?i=integral+1%2F%28%28x^2-9%29^%281%2F2%29%29+dx this is wht Wolfram. says :/

Answer 10

you guys are unbelievable. where I been all these days?

Answer 11

But this online stuff says like this,
http://www.numberempire.com/definiteintegralcalculator.php

Answer 12

the trick for integrating sec(x) is multiply by (sec(x)+tan(x))/(sec(x)+tan(x))
let u = sec(x) +tan(x)

Answer 13

But assigning x=3 sec@ confuses how boundary limits changes. it doesnt give any answer.

Answer 14

hmm, you have to use trig substitution though
you have to replace @ with x at the end to evaluate
@ = sec^-1(x/3)
it will be a little messy

Answer 15

after substituting in i get:
\[\ln (\frac{\sqrt{x^{2}-9}}{3}+\frac{x}{3})\]

Answer 16

dumbcow, I tried as you said, I am getting boundary condition pi/6 to pi/4. and answer of integral is ln(x). so once boundary condition applied, then answer is 0.405. am not sure this is right.

Answer 17

oh i didn't change the boundary condition since i converted everything back to x

Answer 18

After evaluating from 3sqrt2 to 2sqrt3
= 0.332

Answer 19

you are exactly right. great dumbcow!!

Answer 20

are you able to get what i got..
ln(u) = ln(sec(@) + tan(@)) = ln(sec@ + sqrt[sec^2@ - 1])
@ = sec^-1(x/3)

Answer 21

sorry guys, I slept inbetween., Oops

Answer 22

thanks for your great ideas.