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Jonask
 2 years ago
integration radicals
Jonask
 2 years ago
integration radicals

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Jonask
 2 years ago
Best ResponseYou've already chosen the best response.1\[\color{blue}{\huge\int_0^1\sqrt[3]{1x^7}\sqrt[7]{1x^3}dx}\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0\[\color{blue}{\int_0^1\sqrt[3]{1x^7}dx\int\sqrt[7]{1x^3}dx}\]

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.1yes but when i do that it still seems ugly

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0do one half at a time

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.1i shud make a u sub \[u=1x^7\]

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.1\[u=1x^7\] \[\int\frac{u^{1/3}}{7x^6}du\]

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.1\[\int\frac{u^{1/3}}{7(1u)^{1/7}}\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0maybe that method isn't going to work

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.1http://www.wolframalpha.com/input/?i=integral+%281x%5E7%29%5E%7B1%2F3%7D%281x%5E3%29%5E%7B1%2F7%7D ugly as well but i think we are supposed to use 'by parts'

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.0where did you get this question?

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.1steward calculus advanved problem

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0what if we use the property integral ( f(x) from x=a to b = f(a+bx) from x= a to b )?

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.1in this case a+b=0+1 int f(1x)=f(x)

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0yep, am not too sure if that'll work though, but probably should work ?

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.1ok i have to go i;ll try it thanks to everyone for the effort

SithsAndGiggles
 2 years ago
Best ResponseYou've already chosen the best response.0According to WA, the definite integral is 0: http://www.wolframalpha.com/input/?i=integrate+%28%281x%5E7%29%5E%281%2F3%29++%281x%5E3%29%5E%281%2F7%29%29+over+%5B0%2C1%5D Maybe there's some detail we're not getting about the function itself.

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.1interesting result maybe this property is because of the function is actually an inverse of itself i mean \[f(x)=\sqrt[3]{1x^7}\] then \[f^{1}(x)=\sqrt[7]{1x^3}\] should this mean anything

Jonask
 2 years ago
Best ResponseYou've already chosen the best response.1\[\int_0^1 f(x)f^{1}(x) \space dx\] \[f(1)=f^{1}(1)=0\]

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.2this is a famous question on M.SE
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