<p>The area bounded by \(y=\{x\}\) (fractional part) and the \(x\)-axis from \(x=0\) to \(x=3\) is: [MAU050]</p>
Step-by-Step Solution
Key Concept: {x} has period 1. On [0,1]: {x}=x. Area over [0,1] = \int_0^1 x dx = 1/2. Total = 3 \cdot (1/2) = 3/2.
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<p>$\{x\}$ has period 1. On each unit interval $[n,n+1)$: $\{x\}=x-n$, which is a sawtooth from 0 to 1.</p>
<p>Area over one period: $\int_0^1 x\,dx=\frac{1}{2}$.</p>
<p>Total area over $[0,3]$: $3\times\frac{1}{2}=\boxed{\frac{3}{2}}$</p>
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Correct Answer: ['B']