Evaluate a definite integral by recognizing a perfect square under a square root and correctly applying the absolute value.

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Evaluating a Definite Integral with a Hidden Absolute Value

The definite integral warmup

\(\int_{0}^{1} \sqrt{x^2 - 6x + 9} \, dx.\)

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What you need first

Factoring quadratic expressions
The definition of absolute value
The power rule for integration
Evaluating definite integrals

What this problem tests

Tests the ability to simplify integrands algebraically and correctly handle the absolute value function over a specific interval.

This is a classic calculus problem designed to test whether a student remembers that the square root of x squared is the absolute value of x, not just x.

Evaluating a Definite Integral with a Hidden Absolute Value

What you need first

What this problem tests

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