A) \[f\]is increasing only in the interval \[\left[ 0,\frac{\pi }{2} \right]\]
B) \[f\]is decreasing in the interval \[[0,\pi ]\]
C) \[f\]attains maximum at \[x=\frac{\pi }{2}\]
D) \[f\]attains minimum at\[x=\pi \]
E) \[f\]attains maximum at\[x=\pi \]
Correct Answer: A
Solution :
\[f(x)=\int_{0}^{x}{\sin t\,}dt\,x\ge 0\] \[\Rightarrow \]\[f(x)=\sin x\] Now, \[f(x)>0\]in\[0<x<\frac{\pi }{2}\] \[\therefore \] \[f(x)\]is increasing in \[0<x<\frac{\pi }{2}\]
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