Verify my distance traveled answer...

[hank]

Here's the velocity function:

v(t) = 1/2 - 1/t^2 over [1, 3]

I come up with an answer of 1/3.

I took the integral of |v(t)| with the limits of 1 and 3.

The book says the anser should be 10/3 - 2*sqrt(2).

 

[pka]

The text is correct:
\(\displaystyle \L \int\limits_1^3 {\left| {\frac{1}{2} - \frac{1}{{x^2 }}} \right|dx} = \int\limits_1^{\sqrt 2 } {\frac{{ - 1}}{2} + \frac{1}{{x^2 }}dx} + \int\limits_{\sqrt 2 }^3 {\frac{1}{2} - \frac{1}{{x^2 }}dx} .\)

 

[hank]

Ok, thanks.

Where did they get the sqrt(2) from?

 

[stapel]

Where did [the tutor] get the sqrt(2) from?

Have you looked at the graph? Have you found the function's zeroes (and thus where the function changes sign, so the absolute-value makes a sharp turn)?

Eliz.