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___.
The area of the figure bounded by the parabola (y−2)2=x−1, the tangent to it at the point with the ordinate x=3, and the x-axis is
The value of the parameter a such that the area bounded by y=a2x2+ax+1, coordinate axes, and the line x=1 attains its least value is equal to
Area bounded by the relation [2x]+[y]=5,x,y>0 is__ (where [.] represents greatest integer funciton).
Consider the function defined implicity by the equation y2−2yesin−1x+x2−1+[x]+e2sin−1x=0(where [x] denotes the greatest integer function).
The area of the region bounded by the curve and the line x=−1 is
Consider curves S1:∣x∣+∣y∣=a,S2:x2+y2=a2andS3: ∣x∣+∣y∣=a. If α is area bounded by S1andS2,β is area bounded by S1andS3andγ is the area bounded by S2andS3, then
Consider the two curves C1:y=1+cosxandC2:y=1+cos(x−α) for α∈(0,2π), where x∈[0,π]. Also the area of the figure bounded by the curves C1,C2,andx=0 is same as that of the figure bounded by C2,y=1,andx=π.
For the values of α, the area bounded by C1,C2,x=0andx=π is