Let A(k) be the area bounded by the curves y=x2−3 and y=kx+2\displaystyle.
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.
If the area enclosed by the curve y=xandx=−y, the circle x2+y2=2 above the x-axis is A, then the value of π16A 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
Find the area of the region bounded by the x-axis and the curves defined by y=tanx(where −3π≤x≤3π)andy=cotx(where 6π≤x≤23π).
A farmer F1 has a land in the shape of a triangle with vertices at P(0,0),Q(1,1)andR(2,0). From this land, a neighboring farmer F2 takes away the region which lies between the side PQ and curve of the from y=xn(n>1). If the area of the region taken away by the farmer F2 is exactly 30% of the area of ΔPQR, then the value of n is ___.