Application of Integrals
Find the area of the region bounded by the ellipse 4x2+9y2=1
Consider two curves C1:y2=4[y]xandC2:x2=4[x]y, where [.] denotes the greatest integer function. Then the area of region enclosed by these two curves within the square formed by the lines x=1,y=1,x=4,y=4 is 38squ˙nits (b) 310squ˙nits 311squ˙nits (d) 411squ˙nits
The area bounded by the curve y=x∣x∣, x-axis and the ordinates x=−1and x=1is given by(A) 0 (B) 31 (C) 32 (D) 34[Hint : y=x2if x>0and y=−x2if x<0].
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.