Math Problem Statement

Evaluate the definite integral \( \int_0^\pi \frac{1}{2} (\cos x + |\cos x|) dx \).

Solution

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Math Problem Analysis

Mathematical Concepts

Integral Calculus
Absolute Value
Piecewise Functions

Formulas

Integral of \( \cos x \): \( \int \cos x \, dx = \sin x + C \)
Integral of a piecewise function involving absolute values.

Theorems

Properties of definite integrals
Absolute value decomposition in integration

Suitable Grade Level

Undergraduate Calculus

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