Question

Let the area of the region bounded by the curves be $y^3=x^2$ and
$y=2–x^{2}be\frac{30+\lambda }{15}$ , then $\lambda$ equals ___

Answer 1

The curves intersect at $x=\pm 1,area=|{\int }_{-1}^1\sqrt[3]{3x^2}-2+x^{2}dx|=\frac{32}{15}then\lambda =2$.