Show that 0 x n e x2 dx converges for all n 0 First observe that x n e x2 x n e x for x 1 Then show that x n e x x 2 for x sufficiently large

Question: Show that 0 x n e x2 dx converges for all n > 0. First observe that x n e x2 < x

Show that ∫^∞₀xⁿe^−x2 dx converges for all n > 0. First observe that xⁿe^−x2 < xⁿe^−x for x > 1.
Then show that xⁿe^−x < x⁻² for x sufficiently large.

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