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
The basic idea is that [itex]\int k*f(x) dx = k*\int f(x) dx[/itex]. 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.