If for a real number \[y,\,\,[y]\] is the greatest integer less than o – McqOptions

MCQOPTIONS

1.	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.	\[\frac{\pi }{2}\]
Answer» D. \[\frac{\pi }{2}\]

Discussion

No Comment Found

Related MCQs

\[\int_{0}^{1}{\frac{{{x}^{7}}}{\sqrt{1-{{x}^{4}}}}dx}\] is equal to[AMU 2000]
On the interval \[\left[ \frac{5\pi }{3},\,\,\frac{7\pi }{4} \right],\] the greatest value of the function \[f(x)=\int_{5\pi /3}^{x}{(6\cos t-2\sin t)\,dt=}\]
\[\int_{-\,\pi }^{\,\pi }{\frac{2x(1+\sin x)}{1+{{\cos }^{2}}x}dx}\] is [AIEEE 2002]
\[\int\limits_{0}^{\pi }{\,\frac{\sin \left( n+\frac{1}{2} \right)\text{ }x}{\sin x}}\,dx\], \[(n\in N)\] equals [Kurukshetra CEE 1998]
If \[f(x)=A\sin \left( \frac{\pi x}{2} \right)+B,\] \[{f}'\left( \frac{1}{2} \right)=\sqrt{2}\] and \[\int_{0}^{1}{f(x)\,dx=\frac{2A}{\pi },}\] then the constants \[A\] and \[B\] are respectively [IIT 1995]
For which of the following values of m, the area of the region bounded by the curve \[y=x-{{x}^{2}}\] and the line \[y=mx\] equals\[\frac{9}{2}\] [IIT 1999]
If \[\int_{0}^{{{t}^{2}}}{xf(x)dx=}\frac{2}{5}{{t}^{5}},\,\,t>0,\]then\[f\left( \frac{4}{25} \right)=\] [IIT Screening 2004]
The numbers P, Q and \[R\] for which the function \[f(x)=P{{e}^{2x}}+Q{{e}^{x}}+Rx\] satisfies the conditions \[f(0)=-1,\] \[{f}'(\log 2)=31\] and \[\int_{0}^{\log 4}{[f(x)-Rx]\,dx=\frac{39}{2}}\] are given by
If \[f(x)=\frac{{{e}^{x}}}{1+{{e}^{x}}},\,\,\,\ {{I}_{1}}=\int_{f(-a)}^{f(a)}{xg\{x(1-x)\}dx}\], and \[{{I}_{2}}=\int_{f(-a)}^{f(a)}{g\{x(1-x))\}dx}\], then the value of \[\frac{{{I}_{2}}}{{{I}_{1}}}\] is [AIEEE 2004]
If \[\int_{0}^{x}{f(t)\,dt}=x+\int_{x}^{1}{t\,f(t)\,dt,}\] then the value of \[f(1)\] is [IIT 1998; AMU 2005]