Question

Evaluate the integral of sqrt(x^2-121) divided by x^3 with respect to x.

Answer 1

with respect to x?

Answer 2

\[\int\limits_{}^{}(\sqrt{x^2 - 121})/x^3 dx\]

Answer 3

However you word dx...

Answer 4

\[\int\limits_{}^{}\frac{x^2-121}{x^3}dx=\int\limits_{}^{}(x^2-121)(x^{-3})\]

Answer 5

dx

Answer 6

x^2-121 is under a square root sign

Answer 7

trig sub then

Answer 8

let x=asec(x)

Answer 9

so x=11sec(theta)

Answer 10

think you can handle it from there?

Answer 11

That's what I did, and I got:
\[(1/22)\sec^{-1}(x/11)-\sqrt{x^2-121}/2x^2 +C \]

but my online homework isn't taking it :(

Answer 12

I don't know if the way I typed it is incorrect, but I just want to check if someone else gets the same answer.

Answer 13

what did you get when you subbed everything in

Answer 14

and cancelled everything

Answer 15

\[1/11\int\limits_{}^{}\tan^{2} \theta/\sec^{2} \theta d{\theta}\]

Answer 16

correct so far

Answer 17

Then:
\[1/11\int\limits_{}^{}\sin^{2}{\theta}/\cos^{2}{\theta} * \cos^{2}{\theta} d{\theta}\]

Answer 18

(1/sec^2(theta) = cos^2(theta) )

Answer 19

Cancel cosines and get 1/11 integrand sin^2(theta) d(theta)

Answer 20

alright so far so good

Answer 21

then I made sin^2 to 1-cos^2

Answer 22

oh and 1/2 on the outside

Answer 23

alright

Answer 24

So:\[(1/11)*(1/2)\int\limits_{}^{}(1-\cos^{2}{\theta})d{\theta}\]
\[(1/22)\int\limits_{}^{}(1-\cos^{2}{\theta})d{\theta}\]
\[(1/22)[{\theta}-(1/2)\sin(2{\theta})] +C\]

Answer 25

Then to convert back to x's, used a right triangle.

Answer 26

yep

Answer 27

in your above answer at the top where did you get x^2

Answer 28

\[{\theta}=\sec^{-1}(x/11)\]
\[\sin{2}{\theta}=2\sin{\theta}\cos{\theta}=(\sqrt{x^2-121}/x)*(11/x)\]

Answer 29

Then times sin2theta by 1/2

Then times both by 1/22 :P

Answer 30

so you got sin(2theta) = 2sinthetacostheta

\[\frac{2}{1}\frac{\sqrt{x^2-121}}{x}*\frac{11}{x}=\frac{22}{1}\frac{\sqrt{x^2-121}}{x^2}\]

Answer 31

Times 1/2, cuz originall it was (1/2)sin^2(theta)

Answer 32

so the 2's cancel= (1/2)*2*sin(theta)cos(theta)

Answer 33

correct hmm

Answer 34

I tried entering it again... I can only submit it twice, but it worked the 2nd time :P I guess it didn't like (sec(x/11)^-1 at first so I used their built-in sec^-1. Ugh so frustrating, but at least I know I'm doing the steps correctly. Thanks for checking.

Answer 35

yep

Answer 36

if it didn't work i would have argued to teacher taht the answer was correct

Answer 37

because that answer is correct

Answer 38

Do you know anything about cylindrical shells? I have an unanswered question I posted earlier :)

Answer 39

cylindrical shells?

Answer 40

volume by c.s.