Let S is the region of points which satisfies y2<16x,x<4andx2−7x+12xy(x2−3x+2)>0. Its area is
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
A curve y = f(x) is such that f(x)≥0andf(0)=0 and bounds a curvilinear triangle with the base [0,x] whose area is proportional to (n+1)th power of f(x)⋅ If f(1)=1 then find f(x).
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
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
Let C1andC2 be the graphs of the functions y=x2andy=2x, respectively, where 0≤x≤1. Let C3 be the graph of a function y=f(x), where 0≤x≤1,f(0)=0. For a point P on C1, let the lines through P, parallel to the axes, meet C2andC3 at Q and R, respectively (see figure). If for every position of P(onC1), the areas of the shaded regions OPQ and ORP are equal, determine the function f(x).