Which of the following is the possible value/values of c for which the area of the figure bounded by the curves `y=sin 2x`, the straight lines `x=pi//6, x=c` and the abscissa axis is equal to 1/2?
A
`-(pi)/(6)`
B
`(pi)/(3)`
C
`(pi)/(6)`
D
none of these
Text Solution
Verified by Experts
The correct Answer is:
B
`"Area OABC"=int_(0)^(pi//2)sin2xdx=1` `"Area OAD"=int_(0)^(pi//6)sin2xdx=(1)/(4)` `because" sin 2x is symmetric about origin, therefore,"` `c=-(pi)/(6)" "(because" area OAD = Area OEF")` `"Now, "int_((pi)/(6))^(c)sin 2xdx=(1)/(2)` `cos 2x=-(1)/(2)` `therefore" "c=(pi)/(3)` `therefore" "c=-(pi)/(6),(pi)/(3)`
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