Final answer:
To find the exact length of the curve y = 4 * 2^(3/2), 0 ≤ x ≤ 1, use the arc length formula and solve the integral.
Step-by-step explanation:
To find the exact length of the curve y = 4 * 2^(3/2), 0 ≤ x ≤ 1, we can use the arc length formula. The formula for arc length is given by:
L = ∫sqrt(1 + (dy/dx)^2) dx
In this case, dy/dx = 4 * 2^(3/2) * (ln2) = 8√2 * ln2. So, the arc length can be calculated as:
L = ∫sqrt(1 + (8√2 * ln2)^2) dx
Integrating this expression from 0 to 1 will give us the exact length of the curve.