Reverse the Order of Integration and Then Evaluate the Integral$\int _ { 0 } ^ { 512 } \int _ { \sqrt [ 3 ] { x } } ^ { 8 } \frac { 1 } { y ^ { 4 } + 1 } d y d x$

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The Answer of Reverse the Order of Integration and Then Evaluate the Integral$\int _ { 0 } ^ { 512 } \int _ { \sqrt [ 3 ] { x } } ^ { 8 } \frac { 1 } { y ^ { 4 } + 1 } d y d x$

Reverse the Order of Integration and Then Evaluate the Integral $\int _ { 0 } ^ { 512 } \int _ { \sqrt [ 3 ] { x } } ^ { 8 } \frac { 1 } { y ^ { 4 } + 1 } d y d x$

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Reverse the Order of Integration and Then Evaluate the Integral ∫0512∫x381y4+1dydx\int _ { 0 } ^ { 512 } \int _ { \sqrt [ 3 ] { x } } ^ { 8 } \frac { 1 } { y ^ { 4 } + 1 } d y d x∫0512​∫3x​8​y4+11​dydx

Definitions:

Reverse the Order of Integration and Then Evaluate the Integral $\int _ { 0 } ^ { 512 } \int _ { \sqrt [ 3 ] { x } } ^ { 8 } \frac { 1 } { y ^ { 4 } + 1 } d y d x$