Answer to Question #224841 in Chemical Engineering for Lokika

Question

Solve ∫y=0^{1}∫x=y^{2}^{1}∫z=0^{1-x}x dzdxdy

Answer 1

$\int _0^1\int _{b^2}^1\int _0^{1-x}xdzdxdy\\ =\int _0^1\int _{y^2}^1x\left(-x+1\right)dxdy\\ =\int _0^1\left(\frac{1-y^4}{2}-\frac{1-y^6}{3}\right)dy\\ =\frac{4}{35}$