Final answer:
To calculate the arc length of the function f(x) over the interval [1, 2], one must use the arc length formula involving integration after finding the derivative of f(x), but the original function provided contains typos that require clarification before proceeding.
Step-by-step explanation:
The student has asked to calculate the arc length of the function f(x) = 1/4x²-1/2 Inx 2 nx over the interval [1, 2]. To calculate the arc length of a function, you typically use the arc length formula:
L = ∫ sqrt(1 + (f'(x))²) dx
f'(x) is the derivative of the function, and you integrate from the lower to upper bounds of the interval. However, there seem to be some typos in the original function, so it's crucial to clarify the function before proceeding. Assuming a correctly written function, let's also assume the derivative has been calculated, and an integral set up. After a correct evaluation of the integral, you would arrive at the arc length.
If the typos in the original function are corrected and the function is given as f(x) = 1/4x² - (1/2)·ln(x), then the calculation involves finding the derivative of f(x), squaring it, adding 1, taking the square root, and integrating the result over the interval [1, 2].