If the curve y=ax1/2+bx passes through the point (1,2) and lies above the x-axis for 0≤x≤9 and the area enclosed by the curve, the x-axis, and the line x=4 is 8 sq. units. Then
Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., x=x(t),y=(t), then the area of the figure is evaluated by one of the three formulas :
Where αandβ are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t.
The area of the region bounded by an are of the cycloid x=a(t−sint),y=a(1−cost) and the x-axis is
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 ___.