Register to reply

Quick integration question

by vorcil
Tags: integration
Share this thread:
vorcil
#1
Apr13-10, 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
Phys.Org News Partner Science news on Phys.org
World's largest solar boat on Greek prehistoric mission
Google searches hold key to future market crashes
Mineral magic? Common mineral capable of making and breaking bonds
rock.freak667
#2
Apr13-10, 08:09 PM
HW Helper
P: 6,206
1/2 is a constant, 1/√h is a constant

it must follow that

1/2√h is constant as well.
Mark44
#3
Apr13-10, 08:14 PM
Mentor
P: 21,215
Quote Quote by vorcil View Post
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.

vorcil
#4
Apr13-10, 08:20 PM
P: 394
Quick integration question

cheers


Register to reply

Related Discussions
Quick question on tables and integration Calculus & Beyond Homework 5
Quick integration question. Calculus & Beyond Homework 4
Quick integration question Calculus & Beyond Homework 1
Quick question about integration Calculus 2
Quick integration question Introductory Physics Homework 3