Question:medium
Let \( f(x) = \max\{x + |x|, x - |x|, x - [x]\} \), where \( [x] \) stands for the greatest integer not greater than \( x \). Then \( \int_{-3}^{3} f(x) \, dx \) has the value:
Let \( f(x) = \max\{x + |x|, x - |x|, x - [x]\} \), where \( [x] \) stands for the greatest integer not greater than \( x \). Then \( \int_{-3}^{3} f(x) \, dx \) has the value:
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When dealing with piecewise functions involving integer and fractional components, it's crucial to carefully assess the contribution from each part. In symmetric intervals, evaluate both positive and negative contributions to ensure accuracy.
Updated On: Nov 28, 2025
- \( \frac{51}{2} \)
- \( \frac{21}{2} \)
- \( 1 \)
- \( 0 \)
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