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Definite Integration question

2022 · 27 Jul · Shift 1 · Q30
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  5. /2022 · 27 Jul · Shift 1 · Q30

Definite Integration question

2022 · 27 Jul · Shift 1 · Q30

JEE MainMathematicsDefinite IntegrationMCQ+4 / −1
Let f:R→Rf: \mathbb{R} \rightarrow \mathbb{R}f:R→R be a function defined as f(x)=asin⁡(π[x]2)+[2−x],a∈Rf(x)=a \sin \left(\frac{\pi[x]}{2}\right)+[2-x], a \in \mathbb{R}f(x)=asin(2π[x]​)+[2−x],a∈R where [t][t][t] is the greatest integer less than or equal to ttt. If lim⁡x→−1f(x)\mathop {\lim }\limits_{x \to -1 } f(x)x→−1lim​f(x) exists, then the value of ∫04f(x)dx\int\limits_{0}^{4} f(x) d x0∫4​f(x)dx is equal to
  1. A
    −-− 1
  2. B
    −-− 2
  3. C
    1
  4. D
    2
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