Area enclosed by the curve y=f(x) defined parametrically as x=1+t21−t2,y=1+t22t is equal to
Consider the function defined implicity by the equation y2−2yesin−1x+x2−1+[x]+e2sin−1x=0(where [x] denotes the greatest integer function).
Line x=0 divides the region mentioned above in two parts. The ratio of area of left-hand side of line to that of right-hand side of line is
Let R be the region containing the point (x, y) on the X-Y plane, satisfying 2≤∣x+3y∣+∣x−y∣≤4. Then the area of this region is
Consider curves y=x21,y=4(x−1)1. Let α be the value of a(a>2) for which area bounded by curves between x=2andx=a is 1/a is e2+1andβ be the of b∈(1,2), for which the area bounded by curves between x=b and x=2 is 1−b1, then