Mass of a Rod

[nikchic5]

The linear density of a rod of length 0.25 m is given by p(x) = (1) / (sqrt x)grams/cm, where x is measured in centimeters from one end of the rod. Find the mass of the rod.

Please help me!! If you could help in anyone I would really apprecite it! Thanks!

 

[Gene]

The incremental mass is p(x)dx =
dx/sqrt(x) = x^(-1/2)dx
Integrate that from x=0 to .25

 

[nikchic5]

I don't understand....

What exaclty do you mean?

 

[Gene]

Take the integral of
x^(-1/2)dx from 0 to .25
I don't know how else to say it.

 

[nikchic5]

??

what do you mean the intergral?[/code]

 

[stapel]

what do you mean the intergral?

If you haven't yet learned about integration (the standard method of solution), then please provide the method you are supposed to use.

Thank you.

Eliz.

 

[nikchic5]

?

Would the answer be 8?

 

[stapel]

Would the answer be 8?

That's not what I'm getting. Please reply showing your steps, including specification of the method you're using.

Thank you.

Eliz.

 

[nikchic5]

Ok

I did (-1/2)x^(-3/2)* 2 which equals 8. Am I right?

 

[stapel]

Re: Ok

I did (-1/2)x^(-3/2)* 2 which equals 8.

For what value of "x" did you evaluate the above expression? And how did you obtain this expression?

Please reply showing all of your steps. Thank you.

Eliz.

 

[nikchic5]

What I used,,,

I used the value 0 which gave me zero and then 0.25 which is what gave me 8. Thanks

 

[stapel]

I used the value 0 which gave me zero and then 0.25 which is what gave me 8.

Assuming you mean that you plugged "0" in for "x" in your posted expression:

. . . . .\(\displaystyle \large{\left(-\frac{1}{2}\right) \,\left(\frac{1}{\sqrt{x^3}}\right) \,(2)\, =\,\frac{-1}{\sqrt{x^3}}}\)

...this can not be evaluated at x = 0, because division by zero is undefined.

How did you obtain this expression? What method are you supposed to be using?

Thank you.

Eliz.