MCQ
$\int\limits_{0}^{5} \cos \left(\pi\left(x-\left[\frac{x}{2}\right]\right)\right) d x$
Where $[t]$ denotes greatest integer less than or equal to $t$, is equal to
- A$-3$
- B$-2$
- C$2$
- ✓$0$
Where $[t]$ denotes greatest integer less than or equal to $t$, is equal to
$\Rightarrow I=\int\limits_{0}^{2} \cos (\pi x) d x+\int\limits_{2}^{4} \cos (\pi x-\pi) d x+\int\limits_{4}^{5} \cos (\pi x-2 \pi) d x$
$\Rightarrow I=\left[\frac{\sin \pi x}{\pi}\right]_{0}^{2}+\left[\frac{\sin (\pi x-\pi)}{\pi}\right]_{2}^{4}+\left[\frac{\sin (\pi x-2 \pi)}{\pi}\right]_{4}^{5}$
$\Rightarrow I=0$
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where $[x]$ is the greatest integer less than or equal to $x$, then the value of $\alpha$ is :