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El_Arrow
 one year ago
stuck on this surface area problem
El_Arrow
 one year ago
stuck on this surface area problem

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El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.1y= (x^(2)/4)(ln(x)/2) 1<x<2 about the yaxis

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.1@freckles @zepdrix @SithsAndGiggles @mathmath333

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.1okay so i got the set up done dw:1443761100902:dw

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.1when i would use usubstitution i would get dw:1443761202970:dw

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.1so my question is what do i do with the (1/4)?

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1\(\large y= \frac{x^2}{4}\frac{ln x}{2}\) ?? if so \(\sqrt{1 + y'^2 } = \sqrt{1 + (\frac{x}{2}\frac{1}{2x})^2} = \sqrt{\frac{x^2}{4}+\frac{1}{4x^2} +\frac{1}{2}} =\frac{x}{2}+\frac{1}{2x}\)

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.1so thats it i dont do any usubstitution? please answer back @IrishBoy123

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1if you are happy with the algebra i have shown, you go straight to the integral. i think it's fine but you should check for yourself. one small correction, which **makes no difference** here, but which might matter elsewhere, is that \(\sqrt{z^2} = z\) so i should have said: \[\sqrt{1 + y'^2 } = \sqrt{1 + (\frac{x}{2}\frac{1}{2x})^2} = \sqrt{\frac{x^2}{4}+\frac{1}{4x^2} +\frac{1}{2}} =\sqrt{\left( \frac{x}{2}+\frac{1}{2x} \right)^2} = \left \frac{x}{2}+\frac{1}{2x} \right\] and here: \(\large \left \frac{x}{2}+\frac{1}{2x} \right = \frac{x}{2}+\frac{1}{2x} \) because \(x>0\)

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1here that is again, this time fitting on the page... \[\sqrt{1 + y'^2 } = \sqrt{1 + (\frac{x}{2}\frac{1}{2x})^2} = \sqrt{\frac{x^2}{4}+\frac{1}{4x^2} +\frac{1}{2}} \\ =\sqrt{\left( \frac{x}{2}+\frac{1}{2x} \right)^2} = \left \frac{x}{2}+\frac{1}{2x} \right\]

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.1so then what do i put for the x @IrishBoy123

El_Arrow
 one year ago
Best ResponseYou've already chosen the best response.1oh so i just multiply the x with the answer we got inside the square root

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.1yes \[ S = 2 \pi \int\limits_{1}^{2} x \left( \frac{x}{2}+\frac{1}{2x} \right) \; dx = \dots \]

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