Question

$∫^5_0\,cos(π(x-[\frac{x}{2}]))dx$, where [t] denotes greatest integer less than or equal to t , is equal to

• A. -3
• B. -2
• C. 2
• D. 0

Answer 1

Answer: (D)

0

Answer 2

The correct option is(D): 0

$∫^5_0\,cos(π(x-[\frac{x}{2}]))dx$

$\frac{\sin\pi{x}}{\pi}|^2_0+\frac{\sin(\pi(x-1))}{\pi}|^4_2+\frac{\sin(\pi(x-2))}{\pi}|^5_4$

= 0 + 0 + 0 = 0