Find the greatest value of `x^2 y^3`, where x and y lie in the first quadrant on the line `3x+4y=5`.

Find the greatest value of x^(3)y^(4) if 2x+3y=7 and x>=0,y>=0 .

Find the area bounded by the cirxle x^2+y^2 =16 and the line y=x in the first quadrant .

Find area of the region bounded by the parabola x ^(2) = 4 y, the Y-axis lying in the first quadrant and the lines y =3.

Find the area bounded by the curve y=4x^(2),x=0,x=1 and y=4 in first quadrant.

Find the least and the greatest value of f(x , y) = x^(2) + y^(2) - xy where x and y are connected by the relation x^(2) + 4y^(2) = 4

Find the area enclosed between circle x^2+y^2=1 and the line x+y=1 in first quadrant.

Find the area bounded by the curve y=sqrtx,x=2y+3 in the first quadrant and X-axis.

Find the area bounded by the curve y=sqrtx,x=2y+3 in the first quadrant and X-axis.

The area of the region bounded by the curve y ^(2) = x and the Y axis in the first quadrant and lines y= 3 and y = 9 " is "_________"

Find the least and greatest value of f(x,y) = x^(2) + y ^(2) - xy where x and y are connected by the relation x^(2)+4y^(2) = 4 .