Question

Let \( f(x)=\max\{x+[x],\, x-[x]\ \), where \( [x] \) is the greatest integer \( \le x \). Then} \[ \int_{-3}^{3} f(x)\,dx \] has the value:

• A. \( \frac{51}{2} \)
• B. \( \frac{21}{2} \)
• C. \( 1 \)
• D. \( 0 \)

Hint:

For floor functions: Split into unit intervals. Treat function as linear on each.

Answer 1

The Correct Option is B