WBJEE · Maths · Definite Integration
Let \(f(x)=\max \{x+|x|, x-[x]\}\), where \([x]\) stands for the greatest integer not greater than \(x\). Then \(\int_{-3}^3 f(x) d x\) has the value
- A \(\frac{51}{2}\)
- B \(\frac{21}{2}\)
- C \(1\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(\frac{21}{2}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & f(x)=\max \cdot\{x+|x|, x-[x]\}=\max \{x+|x|,\{x\}\} \\ & \int_{-3}^3 f(x) d x \\ & =\int_{-3}^0\{x\} d x+\int_0^3 2 x d x \\ & =\frac{3}{2}+9=\frac{21}{2}\end{aligned}\)
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