In Fig. 4.176, `X Y A C` and `X Y` divides triangular region `A B C` into two parts equal in area. Determine `(A X)/(A B)dot`

In Figure, B C X Y ,\ B X C A and A B Y Cdot Prove that: a r( A B X)=a r( A C Y)

Consider a region R={(x,y) in R^(2):x^(2) le y le 2x} . If a line y= alpha divides the area of region R into two equal parts, then which of the following is true.?

In Fig.76, A B C Ddot\ Find the value of x , y , zdot

Let C_(1 )and C_(2) be two curves passing through the origin as shown in the figure. A curve C is said to ‘‘bisect the area’’ the region between C_(1) and C_(2) , if for each point P of C, the two shaded regions A and B shown in the figure have equal areas. Determine the upper curve C_(2) , given that the bisecting curve C has the equation y = x^(2) and that the lower curve C_(1) has the equation y = x^(2)//2.

The area between x=y^(2) and and is divided into two equal parts by the line x=a find the value of a.

The area between the curve x=y^(2) and x=4 which divide into two equal parts by the line x=a. Find the value of a

Using integration find the area of the triangular region whose sides have equations y=2x+1,y=3x+1 and x=4

The figure shows a portion of the graph y=2x-4x^(3) . The line y=c is such that the areas of the regions marked I and II are equal. If a, b are the x-coordinates of A,B respectively, then a+b equals-

Using integration find the area of the triangular region whose sides have the equations y=2x+1y=3x+1 and and x=4

Area bounded by curve y^(2)=x and x=4 is divided into 4 equal parts by the lines x=a and y=b then a& b is