Find the area included between the line `y=x` and the parabola `x^2=4y`.

Find the shortest distance between the line y=x-2 and the parabola y=x^(2)+3x+2

Find the shortest distance between the line y=x-2 and the parabola y=x^(2)+3x+2

Find the shortest distance between the line y=x-2 and the parabola y=x^(2)+3x+2

Find the area included between the curves y=x^2 and y=x^3 .

Find the area,lying above the x=axis and included between the circle x^(2)+y^(2)=8x and the parabola y^(2)=4x

Find the area lying above x-axis and included between the circle x^(2)+y^(2)=8x and the parabola y^(2)=4x

Find the area included between the curves x^2=4y and y^2=4x .

Using integration, find the area of the region bounded between : (i) the line x =2 and the parabola y ^(2) = 8x (ii) the line x=3 and the parabola y ^(2) =4x.