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F(x)=int(0)^(x)(cost)/((1+t^(2)))dt0lt=x...

F(x)=`int_(0)^(x)(cost)/((1+t^(2)))dt0lt=xlt=2pi`. Then

A

F is increasing in `((pi)/(2),(3pi)/(2))` and decreasing in `(0,(pi)/(2))` and `((3pi)/(2),2pi)`

B

F is increasing in `(0,pi)` and decreasing in `(pi,2pi)` .

C

F is increasing in `(pi,2pi)` and decreasing in `(0,pi)`

D

F is increasing in `(0,(pi)/(2))` and `((3pi)/(2),2pi)` and decreasing in `((pi)/(2),(3pi)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
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