12th Class
Mathematics
Definite Integrals
Question Bank
Critical Thinking
question_answer
If for a real number \[y,\,\,[y]\] is the greatest integer less than or equal to \[y,\] then the value of the integral \[\int\limits_{\pi /2}^{3\pi /2}{[2\sin x]\,dx}\] is [IIT 1999]
A)\[-\pi \]
B)0
C)\[-\frac{\pi }{2}\]
D)\[\frac{\pi }{2}\]
Correct Answer:
C
Solution :
We know \[-1\le \sin x\le 1\Rightarrow -2\le 2\sin x\le 2\]