The area bounded between the parabolas x2=4yandx2=9y and the straight line y=2 is
If the area bounded by the curve y=x2+1 and the tangents to it drawn from the origin is A, then the value of 3A is __.
Let f(x) be a non-negative continuous function such that the area bounded by the curve y=f(x), the x-axis, and the ordinates x=4πandx=β>4π is βsinβ+4πcosβ+2β. Then f′(2π) is
If the area bounded by the x-axis, the curve y=f(x),(f(x)>0) and the lines x=1,x=b is equal to b2+1−2 for all b>1, then find f(x).
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
The area enclosed by f(x)=12+ax±x2 coordinates axes and the ordinates at x=3(f(3)>0) is 45 sq. units. If m and n are the x-axis intercepts of the graph of y=f(x), then the value of (m+n+a) si ___.
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__.