What is the arclength of #f(x)=x^2e^(1/x)# on #x in [0,1]#?

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What is the arclength of #f(x)=x^2e^(1/x)# on #x in [0,1]#?

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Answer 1 · 2016-09-18T05:57:12

#oo#

Explanation:

Without calculation, we can see easily that #lim_(x->0^+)x^2e^(1/x)=oo#, meaning #f(x)# has a vertical asymptote at #x=0#, and so the arclength must be infinite on #[0, 1]#.

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What is the arclength of #f(x)=x^2e^(1/x)# on #x in [0,1]#?

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