Application of Integrals
Find the area of the region bounded by the curves y=x2+2, y=x,x=0andx=3.
For a point P in the plane, let d1(P)andd2(P) be the distances of the point P from the lines x−y=0andx+y=0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2≤d1(P)+d2(P)≤4, is
The area bounded by the curves y=f(x), the x-axis, and the ordinates x=1andx=b is (b−1)sin(3b+4). Then f(x) is. (a) (x−1)cos(3x+4) (b) sin(3x+4)sin(3x+4) (c) 3(x−1)cos(3x+4) (d) None of these
Draw a rough sketch of the curves y=sinx and y=cosx, as x varies from 0 to 2π, and find the area of the region enclosed between them and the x-axis.
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 of the figure bounded by the parabola (y−2)2=x−1, the tangent to it at the point with the ordinate x=3, and the x−aξs is 7squ˙nites (b) 6squ˙nites 9squ˙nites (d) None of these