Find the area of the region lying between the parabolas ` 4 y ^2 = 9 x and 3 x ^ 2 = 16 y`.

(a) Draw the rough sketch and find the area of the region included between the parabolas : (i) y ^(2) = 4x and x ^(2) = 4y (ii) y ^(2) = 9x and x ^(2) - 9y (iii) y ^(2) = 16x and x ^(2) = 16y. (b) Find the ratio in which the area bounded by the curves y ^(2) = 12x and x ^(2) = 12y is divided by the line x =3.

Find the area of the region between the parabola x=4y-y^(2) and the line x=2y-3

Find the area of the region between the parabola x=y^(2)-6y and the line x=-y

Find the area of the region included between the parabola y^(2)=x and the line x+y=2 .

Find the area of the region included between the parabolas y^(2)=4ax and x^(2)=4ay, where a>0

Find the are of the region included between the parabola y^2= 3x and the circle x^2+y^2 - 6x =0 lying in the first quadrant

Find the area of the region bounded by the parabola y=x^(2) and y=|x|

Find the area of the region bounded by the parabola y=x^(2) and y=|x|

Find the area of the region bounded by the parabola y ^ 2= 16 x and the line x = 4 .

The area of the region included between the parabolas y^(2) = 16x and x^(2) = 16y , is given by …….. sq.units