# Math Help - finding lengths of curves

1. ## 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?

2. To compute arc length you must integrate $1+(\frac{dy}{dx})^2$ over the indicated interval.
To compute arc length you must integrate $1+(\frac{dy}{dx})^2$ over the indicated interval.
Actually, it's $\displaystyle \sqrt{1 + \left(\frac{dy}{dx}\right)^2}$ that you need to integrate.
4. $\displaystyle S = \int_a^b \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx$