If `S` is the sum of possible 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,` then the value of `pi//S` is____

Answer

6

Explanation

`"Area "OABC=overset(pi//2)underset(0)intsin 2x dx =1`
`"Area "OAD =overset(pi//6)underset(0)intsin 2x dx =(1)/(4)`
Since sin 2x is symmetric about origin,
`"so "c=-(pi)/(6)," because area" OAD =" area "OEF`
`overset(c)underset((pi)/(6))intsin 2x dx =(1)/(2)`
`cos 2c =-(1)/(2) cos 2c =(3)/(2)` (not posible)
`c=(pi)/(3)`
`"so "c=-(pi)/(3),(pi)/(3)`