Evaluate the triple iterated integral. $$ \int_1^6 \int_0^1 \int_0^{x^4} 5ze^{-x^5} dy dx dz $$
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Step 1: First, we integrate with respect to $y$: $$ \int_0^{x^4} 5ze^{-x^5} dy = 5ze^{-x^5} \int_0^{x^4} dy = 5ze^{-x^5} [y]_0^{x^4} = 5ze^{-x^5} x^4 = 5x^4 z e^{-x^5} $$ Show more…
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