Final answer:
To find the length of the curve y = 3/5x⁵/³ - 3/4x¹/³ + 8 for the interval 1 ≤ x ≤ 8, we need to use the formula for arc length of a curve.
Step-by-step explanation:
To find the length of the curve y = 3/5x⁵/³ - 3/4x¹/³ + 8 for the interval 1 ≤ x ≤ 8, we need to use the formula for arc length of a curve. The formula is:
Length = ∫√(1+(dy/dx)²) dx
First, we need to find the derivative of the given function y with respect to x, and then substitute it into the arc length formula. Finally, evaluate the integral over the given interval.