The area enclosed by the curve y=4−x2,y≥2sin(22xπ, and the x-axis is divided by the y-axis in the ratio
If a(a>0) is the value of parameter for each of which the are of the figure bounded by the straight line y=1+a4a2−ax and the parabola y=1+a4x2+2ax+3a2 is the greatest, then the value of a4 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___.
The value of a(a>0) for which the area bounded by the curves y=6x+x21,y=0,x=a,andx=2a has the least value is ___.
If the area enclosed by curve y=f(x)andy=x2+2 between the abscissa x=2andx=α,α>2,is(α3−4α2+8) sq. units then find function f(x). It is known that curve y=f(x) lies below the parabola y=x2+2.
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