Home
Class 12
MATHS
If S is the sum of possible values of c ...

If `S` is the sum of possible values of `c` for which the area of the figure bounded by the curves `y=s in2x ,` the straight lines `x=pi/6,x=c ,` and the abscissa axis is equal to `1/2,` then the value of `pi//S` is____

Text Solution

Verified by Experts

The correct Answer is:
6

`"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)`
Promotional Banner

Topper's Solved these Questions

  • AREA

    CENGAGE|Exercise JEE Main Previous Year|10 Videos

  • AREA

    CENGAGE|Exercise JEE Advanced Previous Year|9 Videos

  • AREA

    CENGAGE|Exercise Exercise (Matrix)|4 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE|Exercise Question Bank|29 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

Similar Questions

Explore conceptually related problems

If S is the sum of possible values of c for which the area of the figure bounded by the cuuves y=sin2x, the straight lines x=(pi)/(6),x=c, and the abscissa axis is equal to (1)/(2), then the value of pi/S is

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?

If S is the sum of cubes of possible value of c for which the area of the figure bounded by the curve y=8x^(2)-x^(5), then straight lines x=1 and x=c and the abscissa axis is equal to (16)/(3), then the value of [S], where [.] denotest the greatest integer function,is

Find the area of the figure bounded by the curve y=sin^-1x , the lines x=0 and y=pi/2 .

Find the value of ‘c’ for which the area of the figure bounded by the curve, y = 8x^(2) – x^(5) , the straight lines x = 1 and x = c and the abscissa axis is equal to 16//3 .

The value of a for which the area of the region bounded by the curve y = sin 2x , the straight lines x = pi//6, x = a and x-axis is equal to 1/2 is-

The value of k for which the area of the figure bounded by the curve y=8x^(2)-x^(5) , the straight line x=1 and x=k and the x-axis is equal to 16//3

Find the area bounded by the curves y=|sin x|, the x-axis and the lines |x|=pi

The area of the region bounded by the curve y = sin x between the ordinates x=0,x=pi/2 and the X-axis is