If the area by `y=x^2+2x-3` and the line `y=k x+1` is the least, find `k` and also the least area.

The area bounded by the parabola y = x^(2) and the line y = 2x is

The value of the parameter a such that the area bounded by y=a^(2)x^(2)+ax+1, coordinate axes, and the line x=1 attains its least value is equal to

Find the area between the line y=x+1 and the curve y=x^(2)-1

Find the area enclosed by the parbola 4y=3x^(2) and the line 2y = 3x + 12 .

Find the area of the region enclosed by the parabola x^(2) = y and the line y = x + 2 and the x-axis.

Find the area of the region bounded by the curve y^(2) = x and the lines x = 1, x = 4 and the x -axis.

Find the area of the region bounded by the line y = 3x +2, the x-axis and the ordinates x = -1 and x = 1.

Find the area bounded by x=1 and x=2 , x axis and the line 4x-3y =12 .

Find the area bounded by the curve x^(2) = 4y and the line x = 4y -2 .

Find the area bounded by the curve x^(2) = 4y and the line x = 4y -2 .