The base of a solid in the xyplane is the first-quadrant region bounded y=x and y=x2.Cross sections of the solid perpendicular to the xaxis are squares.What is the volume,in cubic units, of the solid?

Answer 1

the bounded region is from (0,0) to (1,1)

since the cross sections of the solid is perpendicular to the x axis and are square

so cross section area is (x-x^{2 )^2}

^{so V=integral from 0-1(x-x^2)^2dx}

^{v=integral (x^2-2x^3+x^4)dx}

^{v=1/3x^3-1/2x^4+1/5x^5]}0¹

v=1/3-1/2+15=1/30 unit^3