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Which of the following is the possible v...

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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