Set $up,$ but $do$ not evaluate, integral$(s)$ for the area $of$ the shaded region $of$ Tschirnhausen's cubic,

which $is$ defined $by{y}^2=x^2(x+3).$ Hint: Solving for $y,$ one obtains $y=+-\sqrt[\phantom{2}]{x^2(x+3)}.$ Consider

these $as$ your two functions and compare $to$ the picture.