Final answer:
To find the length of the curve, we need to use the arc length formula. The arc length formula for a curve y=f(x) from a to b is given by...
Step-by-step explanation:
To find the length of the curve, we need to use the arc length formula. The arc length formula for a curve y=f(x) from a to b is given by:
L = ∫a b √(1 + (f'(x))2) dx
Using this formula for the given curve y = (3/4)x4/3 - (3/8)x2/3 + 6, the limits of integration are 1 and 27. The derivative of the function is f'(x) = (4/3)(3/4)x1/3 - (2/3)(3/8)x-1/3, which simplifies to f'(x) = 2x1/3 - x-1/3. Plugging these values into the formula:
L = ∫1 27 √(1 + (2x1/3 - x-1/3)2) dx
This integral can be solved using integration techniques to find the exact length of the curve.