Question

The value of $\int\limits_0^1 \cos ([2 x] \pi) \cos (\pi x) d x$ is equal to
[Note: $[x]$ denotes the largest integer less than or equal to $x$.

• A. 1
• B. $\frac{-2}{\pi}$
• C. $\frac{2}{\pi}$
• D. $\frac{1}{\pi}$

Answer 1

Answer: (C)

$\int\limits_0^1 \cos ([2 x] \pi) \cos (\pi x) d x=\int\limits_0^{1 / 2} \cos \pi x d x+\int\limits_{1 / 2}^1(-\cos \pi x) d x=\frac{1}{\pi}+\frac{1}{\pi}=\frac{2}{\pi}$