The positive valu of the parameter 'k' for which the area of the figure bounded by the curve y=sin(kx),x=3k2π,x=3k5π and x-axis is less than 2 can be
Consider two regions
R1:points P are nearer to (1,0) than to x=−1.
R2:Points P are nearer to (0,0) than to (8,0) Find the area of the region common to R1andR2.
Let C be a curve passing through M(2,2) such that the slope of the tangent at any point to the curve is reciprocal of the ordinate of the point. If the area bounded by curve C and line x=2 is A, then the value of 23A is__.
Let S be the area bounded by the curve y=sinx(0≤x≤π) and the x-axis and T be the area bounded by the curves y=sinx(0≤x≤2π),y=acosx(0≤x≤2π), and the x-axis (where a∈R+). The value of (3a) such that S:T=1:31 is___.
If S is the sum of cubes of possible value of c for which the area of the figure bounded by the curve y=8x2−x5, then straight lines x=1 and x=c and the abscissa axis is equal to 16/3, then the value of [S], where [.] denotes the greatest integer function, is ___.
Two curves C1≡[f(y)]2/3+[f(x)]1/3=0andC2≡[f(y)]2/3+[f(x)]2/3=12, satisfying the relation (x−y)f(x+y)−(x+y)f(x−y)=4xy(x2−y2)
The area bounded by C1andx+y+2=0 is