Saturday

September 20, 2014

September 20, 2014

Posted by **Krystal** on Thursday, October 19, 2006 at 3:56am.

y=lnx, (squareroot)3/3 greater than or equal to x less than or equal to 1

It sounds as if you want the length of the y = ln x curve from

x = sqrt(3)/3 (0.57735..) to 1.

The formula for the arc length of a line y(x) is

Length = (INTEGRAL OF) sqrt [1 + (dy/dx)^2] dx

In your case dy/dx = 1/x

so Length = (INTEGRAL OF) sqrt [1 + 1/x^2] dx

Perform the integration between your indicated limits for the answer. I find the integration easier to perform by making the substitution u = 1/x. It's a bit messy.

I have sqrt [1 + 1/x^2] dx , I just don't know what to do next...

Make the substitutions 1/x = u and

dx = u^-2 du

Then the integral becomes

INTEGRAL -[sqrt(1 + u^2)]/u^2 du

According to my table of integrals, the indefinite integral is

[sqrt (1 + u^2)]/u - ln[u + sqrt (u^2 = 1)]

The second term can also be expressed as an arcsinh function.

Integrate that between the two values of u that correspond to your x limits.

Here's a useful site I use to check integrals:

integrals.wolfram. c o m

(delete the spaces)

That's the Wolfram integrator, which is actually Mathematica, a fairly good piece of software for finding anti-derivatives.

When I check sqrt(1 + 1/x^2) I got a slightly different anti-derivative, just thought I'd mention this.

**Answer this Question**

**Related Questions**

math - State the null hypothesis, Ho, and the alternative hypothesis, Ha, that ...

calculus - Consider the function f(x)=65x−cos(x)+2 on the interval 0 less ...

Math - I'm having a hard time with graphing this problem. Could someone please ...

Rational Inequality with Absolute Value - Here's a question I'm having trouble ...

Math - I already posted this, but wanted to say that I have the answers and it ...

Algebra - Use a graphing calculator or a computer to graph the system of ...

Calculus - Consider the function f(x)=6x-cos(x)+5 on the interval 0 is less than...

Algebra--Correction? - Solve x^2 -3x is greater than or equal to 10 Would the ...

random variables - For the standard normal random variable Z, compute the ...

math - sketch the feasible region for this system of the inqualities and find ...