Curious Integrals

Calculus Level 2

If A=01(1x1/p)qdxA=\int _{ 0 }^{ 1 }{ { \left( 1-{ x }^{ 1/p } \right) }^{ q } } dx and B=01(1x1/q)pdx,B=\int _{ 0 }^{ 1 }{ { \left( 1-{ x }^{ 1/q } \right) }^{ p} } dx, for p>0p > 0 and q>0q > 0, what is the value of AB?A - B?

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