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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
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Then where do you needhelp with?
Evaluating
Where do you people get your bike avatars from?

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Other answers:

I do not want "Google" as an answer... :O
looks trig sub...have you learned that yet?
Yes
but we really did gust google this! i swear! :(
What's the whole question?
just*
|dw:1337521244254:dw|
|dw:1337521266266:dw|
Yes I know that trig sub.
|dw:1337521291094:dw|
But ultimately, you have to put a -4 into a trigonometric function's argument. How will that work?
the problem is subbing in the limits???
convert the limits when using the trig sub
dont forget to change back to x before evaluating
No, you don't need to convert back
otherwise you'll have to convert the limits in terms of theta
Ok let me see what happens: - tan(θ) = u/1 - sec(θ) = \sqrt{1 + u^2} Then, sec^2(θ)dθ = du
yep.. \[\int \sec^3 \theta d\theta\]
Then what is limits of integration wrt θ?
What is arctan(-4)?
How did you get that?
I got sec^3(θ)
it was sec^3 theta...ohh woops
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
|dw:1337523905957:dw| @LagrangeSon678 @shivam_bhalla
evaluate it individually .. \[ \int \sec \theta d\theta = \ln |\sec\theta + \tan\theta|\]
this is a lot better http://answers.yahoo.com/question/index?qid=20110524035942AAXxTdM
@QRAwarrior , i just remember this \[\int\limits_{}^{}\sqrt{x^2+a^2} = \frac{x}{2}\sqrt{x^2+a^2}+\frac{a^2}{2}\log{|x+\sqrt{x^2+a^2}|}+C\]
You can go ahead and derive this
I forgot the dx in the question :P
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...
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!!
brb
slight Correction: \[\int\limits\limits_{}^{}\sqrt{x^2+a^2} \space \space dx = \frac{x}{2}\sqrt{x^2+a^2}+\frac{a^2}{2}\log{|x+\sqrt{x^2+a^2}|}+C\]
@shivam_bhalla look at my recent post above
Those are two functions!
I just realized! I would have to use the washer.
@QRAwarrior , I am not so good at this. @TuringTest can surely help you in this :)
Alright thanks your help for the above.
@FoolForMath would you mind helping me here?
Someone is bound to come!
@apoorvk help please?
Please look at the most recent question (it is the one with the sketch just above, NOT THE OPENING POST)
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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