# finding lengths of curves

• Nov 26th 2010, 04:12 AM
berto
finding lengths of curves
simple question of two problems that are alike

1
the interval is 5 ≤ x ≤ 7, the function is y = [(x^4)/4] + [1/(8x^2)]

here, i just integrate function from 5 to 7, correct?

2
the interval is 1≤ x ≤ 9, but i am given an integral from one to x of √[(t^3) - 1]dx

i just replace x with 9 and evaluate, correct?

• Nov 26th 2010, 05:33 AM
DrSteve
To compute arc length you must integrate $\displaystyle 1+(\frac{dy}{dx})^2$ over the indicated interval.
• Nov 26th 2010, 05:36 AM
Prove It
Quote:

Originally Posted by DrSteve
To compute arc length you must integrate $\displaystyle 1+(\frac{dy}{dx})^2$ over the indicated interval.

Actually, it's $\displaystyle \displaystyle \sqrt{1 + \left(\frac{dy}{dx}\right)^2}$ that you need to integrate.
• Nov 26th 2010, 05:36 AM
skeeter
$\displaystyle \displaystyle S = \int_a^b \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx$
• Nov 26th 2010, 06:41 AM
DrSteve
Yep - I accidentally left off the square root - sorry about that.