Find the area bounded by the curve x=⎩⎨⎧−2−y,y3,2−y,y<−1−1≤y≤1y>1 and x=0 is
Find a continuous function f, where (x4−4x2)≤f(x)≤(2x2−x3) such that the area bounded by y=f(x),y=x4−4x2, the y-axis, and the line x=t, where (0≤t≤2) is k times the area bounded by y=f(x),y=2x2−x3, y-axis, and line x=t(where 0≤t≤2).
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
Let Ar be the area of the region bounded between the curves y2=(e−kr)x(where k>0,r∈N) and the line y=mx(where m=0), k and m are some constants
A1,A2,A3,… are in G.P. with common ratio