Let's find a recurrence relation for The base case is 1 where The recurrence relation is...

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Let's find a recurrence relation for The base case is 1 where The recurrence relation is used to relate In to the base case Io. To achieve this we must successively reduce the value of n using integration by parts. Assuming n ≥ 1: Io √ ² zº e-º dx = 2² = xe u = xn u' where = In = 6₁² 2³e-7 dz. [uv] 1 •Souv'dz In • v=e=x • V = Note the strategic choice of u ensures the power an is reduced. With these choices of u,v we have = 1 = [₁² 2¹²e-² da = ₁² w dz So uv' 1 In = [uv] - [² u' vdx uv dx=nIn-1 & P Let's find a recurrence relation for The base case is 1 where The recurrence relation is used to relate In to the base case Io. To achieve this we must successively reduce the value of n using integration by parts. Assuming n ≥ 1: Io √ ² zº e-º dx = 2² = xe u = xn u' where = In = 6₁² 2³e-7 dz. [uv] 1 •Souv'dz In • v=e=x • V = Note the strategic choice of u ensures the power an is reduced. With these choices of u,v we have = 1 = [₁² 2¹²e-² da = ₁² w dz So uv' 1 In = [uv] - [² u' vdx uv dx=nIn-1 & P

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