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Quick integration questionby vorcil
Tags: integration 
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#1
Apr1310, 08:05 PM

P: 394

I need to figure out,
[tex] \int_0^h \frac{1}{2\sqrt{hx}}dx [/tex] If h is a constant, how do i do this? my book shows that I can pull out, [tex] \frac{1}{2\sqrt{h}} \int \frac{1}{\sqrt{x}}dx [/tex] How does the 2 from [tex]\frac{1}{2\sqrt{hx}} [/tex] come out with the [tex]\sqrt{h}[/tex]? I thought I would've only been able to pull out 1/root h, like this, [tex] \frac{1}{\sqrt{h}} \int \frac{1}{2\sqrt{x}}dx[/tex]  why does 2 root h get assigned constant? instead of only h 


#2
Apr1310, 08:09 PM

HW Helper
P: 6,202

1/2 is a constant, 1/√h is a constant
it must follow that 1/2√h is constant as well. 


#3
Apr1310, 08:14 PM

Mentor
P: 21,258

The rest in your problem is just algebra. [tex]\frac{1}{2\sqrt{hx}} = \frac{1}{2*\sqrt{h}\sqrt{x}} = \frac{1}{2\sqrt{h}} \frac{1}{\sqrt{x}}[/tex] Integration is being done with respect to x (i.e., with x as the variable), so h is just another constant in this process. 


#4
Apr1310, 08:20 PM

P: 394

Quick integration question
cheers



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