Draw a rough sketch of the curves `y = (x-1)^2` and `y = |x-1|`. Hence, find the area of the region bounded by these curves.

Draw the rough sketch of the curve y=x^(4)-x^(2) .

Draw a rough sketch of the curve y= (x-1)^2(x-2)(x-3)^3

Draw a rough sketch of the curves y^2 = x + 1 and y^2 =-x+1 and find the area enclosed between them,

Draw the rough sketch of the curve y=(x-1)^(2)(x-3)^(3) .

Draw a rough sketch of the given curve y=1+abs(x+1),x=-3, x=3, y=0 and find the area of the region bounded by them, using integration.

Draw a rough sketch of the curves y^2 = x and y^2 = 4 – 3x and find the area enclosed between them.

Using integration, find the area of the region bounded by the curves y=x and y=x^(3) .

Draw a rough sketch of the curves y =sin x varies from 0 to pi/2 and find the area of the region enclosed by them and x-axis

Draw a rough sketch of the curves y=sinx and y=cosx as x varies from 0 to pi/2 . Find the area of the region enclosed by the curves and the y-axis.

Find the area of the region bounded by the curves x=2y-y^2 and y=2+x .