anonymous
  • anonymous
Horrific integration question help!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
dan815
  • dan815
lol give it to me
dan815
  • dan815
if i see more than 3 trig expressions i am leaving
dan815
  • dan815
if i see more than 1! iam leaving

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More answers

anonymous
  • anonymous
Its to do with the arc length - y=2x^2+4 between x=0 and x=3 .... Got to \[\int\limits_{}\sqrt{1+16x^2}{}\] Between x=3 and x=0 I think i need a hyperbolic substitution??!!
dan815
  • dan815
...
dan815
  • dan815
|dw:1371032528716:dw|
anonymous
  • anonymous
ok thanks, so i dont use dy/dx = 4x?
dan815
  • dan815
u did the arc length formula wrong
dan815
  • dan815
no u didnt! i did it wrong
anonymous
  • anonymous
ah ok i used|dw:1371032776899:dw|
dan815
  • dan815
|dw:1371032809566:dw|
anonymous
  • anonymous
yup agreed, where do i go from there? do i need a U?
dan815
  • dan815
u need hyperbolic subs
anonymous
  • anonymous
thats the bit i'm working on, i really dont understand them though
dan815
  • dan815
before we do that.. have u tried by parts or anything
dan815
  • dan815
lemme check wolfram they usually have interesting ways lol
dan815
  • dan815
woah they did some ridiculous things
anonymous
  • anonymous
i know :( i have a solution here
anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
do u know where any of this comes from?
dan815
  • dan815
well thats beautiful solution...
dan815
  • dan815
sinh^2-cosh^2=1
dan815
  • dan815
isnt there a mistake in there tho
anonymous
  • anonymous
ok, why are they subbing sin-1h ? i know the derivative of sin-1h = \[\frac{ 1 }{\sqrt{1+x^2} }\]
dan815
  • dan815
so how do they still have sinh^2?
dan815
  • dan815
what is du?
dan815
  • dan815
oh i see okay i got it
dan815
  • dan815
|dw:1371033808940:dw||dw:1371033830195:dw|
dan815
  • dan815
and this is a trig identity cosh^2=1+cosh2u
dan815
  • dan815
https://en.wikipedia.org/wiki/Hyperbolic_function
dan815
  • dan815
its all there
anonymous
  • anonymous
|dw:1371034277164:dw|
anonymous
  • anonymous
BINGO
anonymous
  • anonymous
4x = sinhu u = arcsinh4x du/dx = 1/ rt(1+4x^2) dx/du = rt(1+4x^2) dx = rt(1+4x^2) du Into integral \[\int\limits_{}\sqrt{1+4x^2}.\sqrt{1+4x^2}du{}\] \[\int\limits_{?}1+\sinh^2u{}\]
anonymous
  • anonymous
thank you dan!!

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