Application of Integrals
Prove that the curves y2=4xand x2=4ydivide the area of the square bounded by x=0,x=4,y=4andy=0into three equal parts.
Let O(0,0),A(2,0),andB(131) be the vertices of a triangle. Let R be the region consisting of all those points P inside OAB which satisfy d(P,OA)≤min[d(p,OB),d(P,AB)] , where d denotes the distance from the point to the corresponding line. Sketch the region R and find its area.
Consider the region formed by the lines x=0,y=0,x=2,y=2. If the area enclosed by the curves y=exandy=1nx, within this region, is being removed, then find the area of the remaining region.
Area of the region bounded by the curve y2=4x, y-axis and the line y=3is
(A) 2 (B) 49 (C) 39 (D) 29