Find the exact arc length of the curve:

Question

3x^(3/2)-1 from x=0 to x=1?

Answer 1

The curve equation is y = 3x^3/2 - 1 and the interval is [0, 1].

The arc length of f(x) between a and b is

y = 3x^3/2 - 1 ⇒ y' = 3*(3/2)x^1/2.

Substitute y' = (9/2)x^1/2, a = 0 and b = 1 in the above formula..

Let 81x + 4 = t² ⇒ 81dx = 2t dt ⇒ dx = (2/81)t dt