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Evaluate the Integral by Reversing the Order of Integration 01arcsinyπ/28cosx1+cos2xdxdy\int _ { 0 } ^ { 1 } \int _ { \arcsin y } ^ { \pi / 2 } 8 \cos x \sqrt { 1 + \cos ^ { 2 } x } d x d y

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Evaluate the integral by reversing the order of integration. 01arcsinyπ/28cosx1+cos2xdxdy\int _ { 0 } ^ { 1 } \int _ { \arcsin y } ^ { \pi / 2 } 8 \cos x \sqrt { 1 + \cos ^ { 2 } x } d x d y

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