Final answer:
To find the arc length for the curve y = 3x² - 1/24lnx, we can use the formula for arc length: L = ∫√(1+(f'(x))²)dx. First, we find the derivative of y, then we square the derivative, and finally, we integrate the expression to find the arc length.
Step-by-step explanation:
To find the arc length for the curve y = 3x² - 1/24lnx, we can use the formula for arc length:
L = ∫√(1+(f'(x))²)dx
First, we need to find the derivative of y:
y' = 6x - 1/(24x)
Next, we square the derivative:
(y')² = (6x - 1/(24x))²
Now, we can find √(1+(f'(x))²):
√(1+(f'(x))²) = √(1 + (6x - 1/(24x))²)
Finally, we integrate this expression to find the arc length:
L = ∫√(1+(f'(x))²)dx = ∫√(1 + (6x - 1/(24x))²)dx