Vault Of Euclid

Arc Length of a Rational Function

Area and arc length core

Find the arc length of the curve $y = \frac{x^4}{8} + \frac{1}{4x^2}$ from $x=1$ to $x=2$.

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What you need first

Basic differentiation rules
Algebraic manipulation of fractions and exponents
Recognizing perfect square trinomials
Evaluating definite integrals

What this problem tests

Tests the ability to apply the arc length formula, manipulate algebraic expressions to form a perfect square, and evaluate a definite integral.

This is a classic Calculus I problem demonstrating the 'perfect square' trick commonly used in arc length exercises to eliminate the square root.

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