anonymous
  • anonymous
Evaluate the definite integral from u = 0 to u = -4 of: \sqrt{1 + u^2} dx As you may have noticed, I have already done U-sub.
Mathematics
chestercat
  • chestercat
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Mimi_x3
  • Mimi_x3
Then where do you needhelp with?
anonymous
  • anonymous
Evaluating
anonymous
  • anonymous
Where do you people get your bike avatars from?

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anonymous
  • anonymous
I do not want "Google" as an answer... :O
lgbasallote
  • lgbasallote
looks trig sub...have you learned that yet?
anonymous
  • anonymous
Yes
lgbasallote
  • lgbasallote
but we really did gust google this! i swear! :(
Mimi_x3
  • Mimi_x3
What's the whole question?
lgbasallote
  • lgbasallote
just*
lgbasallote
  • lgbasallote
|dw:1337521244254:dw|
anonymous
  • anonymous
|dw:1337521266266:dw|
anonymous
  • anonymous
Yes I know that trig sub.
lgbasallote
  • lgbasallote
|dw:1337521291094:dw|
anonymous
  • anonymous
But ultimately, you have to put a -4 into a trigonometric function's argument. How will that work?
Mimi_x3
  • Mimi_x3
the problem is subbing in the limits???
anonymous
  • anonymous
convert the limits when using the trig sub
lgbasallote
  • lgbasallote
dont forget to change back to x before evaluating
Mimi_x3
  • Mimi_x3
No, you don't need to convert back
lgbasallote
  • lgbasallote
otherwise you'll have to convert the limits in terms of theta
anonymous
  • anonymous
Ok let me see what happens: - tan(θ) = u/1 - sec(θ) = \sqrt{1 + u^2} Then, sec^2(θ)dθ = du
lgbasallote
  • lgbasallote
yep.. \[\int \sec^3 \theta d\theta\]
anonymous
  • anonymous
Then what is limits of integration wrt θ?
anonymous
  • anonymous
What is arctan(-4)?
anonymous
  • anonymous
How did you get that?
anonymous
  • anonymous
I got sec^3(θ)
lgbasallote
  • lgbasallote
it was sec^3 theta...ohh woops
lgbasallote
  • lgbasallote
sec^3 theta = (sec^2 theta)sec theta (1+ tan^2 theta) sec theta \[\int \sec \theta + \tan^2 \theta \sec \theta\] lol got me stuck now
anonymous
  • anonymous
|dw:1337523905957:dw| @LagrangeSon678 @shivam_bhalla
anonymous
  • anonymous
experimentX
  • experimentX
evaluate it individually .. \[ \int \sec \theta d\theta = \ln |\sec\theta + \tan\theta|\]
experimentX
  • experimentX
this is a lot better http://answers.yahoo.com/question/index?qid=20110524035942AAXxTdM
anonymous
  • anonymous
@QRAwarrior , i just remember this \[\int\limits_{}^{}\sqrt{x^2+a^2} = \frac{x}{2}\sqrt{x^2+a^2}+\frac{a^2}{2}\log{|x+\sqrt{x^2+a^2}|}+C\]
anonymous
  • anonymous
You can go ahead and derive this
anonymous
  • anonymous
I forgot the dx in the question :P
anonymous
  • anonymous
Ok, skrew that question and instead would you mind looking at this: You have the curves x = (y-7)^2, and x = 4 that enclose a region. You must rotate this region about y = 5. |dw:1337525316103:dw| I need to use the shell method here, but it looks like as if I will get two cylinders here. Thanks for the help on the opening post question...
experimentX
  • experimentX
I think that's formula for standard integral ... what do we call it ... i have bunch of them in my books ... but they are derived in the same way!!
experimentX
  • experimentX
brb
anonymous
  • anonymous
slight Correction: \[\int\limits\limits_{}^{}\sqrt{x^2+a^2} \space \space dx = \frac{x}{2}\sqrt{x^2+a^2}+\frac{a^2}{2}\log{|x+\sqrt{x^2+a^2}|}+C\]
anonymous
  • anonymous
@shivam_bhalla look at my recent post above
anonymous
  • anonymous
Those are two functions!
anonymous
  • anonymous
I just realized! I would have to use the washer.
anonymous
  • anonymous
@QRAwarrior , I am not so good at this. @TuringTest can surely help you in this :)
anonymous
  • anonymous
Alright thanks your help for the above.
anonymous
  • anonymous
anonymous
  • anonymous
@FoolForMath would you mind helping me here?
anonymous
  • anonymous
Someone is bound to come!
anonymous
  • anonymous
@apoorvk help please?
anonymous
  • anonymous
Please look at the most recent question (it is the one with the sketch just above, NOT THE OPENING POST)
experimentX
  • experimentX
http://www.wolframalpha.com/input/?i=x+%3D+%28y-7%29^2%2C++x%3D4 \[ \int_{5}^{9}2\pi (y-7)(y-7)^2 dy\]

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