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anonymous
 one year ago
how do you integrate sqrt(8x^2)
anonymous
 one year ago
how do you integrate sqrt(8x^2)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442604743169:dw

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1that's\[\int \sqrt{8} \, \sqrt{x^2} \, dx\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how would do this using u subs

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1\[\sqrt{8} = ??\] \[\sqrt{x^2} = ??\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442605850479:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442605975556:dw

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1yes, 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

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Yeah I definitely think it's a trap :P

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i 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

Empty
 one year ago
Best ResponseYou've already chosen the best response.2I 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

Empty
 one year ago
Best ResponseYou've already chosen the best response.2Cool so was that all no questions?! :O

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0there are lol ill try to do them myself and if i cant ill come back for help

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1ah! thanks a million, @Empty

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do i integrate this now dw:1442608670564:dw

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1@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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