Find the area bounded by the curve f(x)=x+sinxand its inverse function between the ordinates x=0 to x=2π.
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 loop described as
If f:[−1,1]→[−21,21],f(x)=1+x2x, then find the area bounded by y=f−1(x),x axis and lines x=21,x=−21.
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__.