请问下面的题目该怎麼用improper integrals解?
请问下面的题目该怎麼用improper integrals解?
An interesting paradox exists in Mathematics with regards to Gabriel's Horn,which is the "horn" generated by revolving the graph of y=1/x about the x-axis over the interval [1,infinite).Find the volume and the surface area of Gabriel's Horn as improper integrals to see what the paradox is.
An interesting paradox exists in Mathematics with regards to Gabriel's Horn,which is the "horn" generated by revolving the graph of y=1/x about the x-axis over the interval [1,infinite).Find the volume and the surface area of Gabriel's Horn as improper integrals to see what the paradox is.
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::∫π(1/x)^2dx=-π∫d(1/x)=-π/x+c
::V=-π/x+c|(1,+∞)=0+π=π
::S=∫2π(1/x)*sqrt(1+(1/x^4))dx
::S->+∞
yes,it's a parodox!A revolving body who has an infinite surface,although it's volume is π,really interesting!
::V=-π/x+c|(1,+∞)=0+π=π
::S=∫2π(1/x)*sqrt(1+(1/x^4))dx
::S->+∞
yes,it's a parodox!A revolving body who has an infinite surface,although it's volume is π,really interesting!
1年前
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