how do you integrate sqrt(8x^2)

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how do you integrate sqrt(8x^2)

Mathematics
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|dw:1442604743169:dw|
that's\[\int \sqrt{8} \, \sqrt{x^2} \, dx\]
how would do this using u subs

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\[\sqrt{8} = ??\] \[\sqrt{x^2} = ??\]
|dw:1442605850479:dw|
|dw:1442605975556:dw|
yes, i would see it that way initially but the problem is i have a feeling that \(\sqrt{x^2}\) is a trap let me ask some others. sorry about this, but i think it might be worthwhile @ganeshie88
ok
Yeah I definitely think it's a trap :P
i try solving this using the u substitution where u=8x^2, du=16x dx and now the problem is i have an x hanging with 16
I don't think a substitution is the right choice here. I think @IrishBoy123 has the right strategy here, separate the constant out front like this: \[\sqrt{8} \int \sqrt{x^2}dx\] The problem is specifically this subtle fact: \[\sqrt{x^2} \ne x\] Here's the proof, let x be some negative number such as -2 why not that's a possible value x can take: \[\sqrt{(-2)^2} = \sqrt{2^2} \ne -2\] So really what we have is the absolute value function! This is kind of tricky to deal with, but easier if you have bounds on your integral: \[\int \sqrt{x^2} dx = \int |x| dx = \int_{-a}^0 -x dx + \int_0^b x dx \] A picture will hopefully clarify this a bit! |dw:1442607260478:dw|
Thank you very much
Cool so was that all no questions?! :O
there are lol ill try to do them myself and if i cant ill come back for help
ah! thanks a million, @Empty
how do i integrate this now |dw:1442608670564:dw|
@magepker728 make a new thread for this new question this one is a tan sub [or maybe, just for fun, a hyperbolic: \(cosh^2(x) − sinh^2(x) = 1 \)].

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