Consider the area S0,S1,S2…. bounded by the x-axis and half-waves of the curve y=e−xsinx, where x≥0.
The sequence S0,S1,S2,…, forms a G.P. with common ratio
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).
Let O(0,0),A(2,0),andB(1,31 be the vertices of a triangle. Let R be the region consisting of all theose points P inside ΔOAB which satisfy d(P,OA)≤ min [d(P,AB)], where d denotes the distance from the point to the corresponding line. Sketch the region R and find its area.