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xartaan
 2 years ago
Integral help, how to approach this?
xartaan
 2 years ago
Integral help, how to approach this?

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xartaan
 2 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{1} \sin(y)(ee^{y^{1/3} })dy\] is the integral. I can plug it into wolfram alpha and get a value, but I would like to know what steps get me there>

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.0Wow. That's an interesting integral. I would suggest distributing the sine function across and take the integral sepearately. e is constant so you can just factor that out. For the second integral, it gets a bit difficult. You could try and work with integration by parts twice.

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0Except that the product of siny and e^y^1/3 is elliptic. Neither of those will differentiate to zero.

xartaan
 2 years ago
Best ResponseYou've already chosen the best response.0Heh, I have a whole homework sheet of these iterated integrals that the inner integral isnt bad, but the insides are just impossible. WA wont even give steps, just values when I include the bounds.. Arg

calmat01
 2 years ago
Best ResponseYou've already chosen the best response.0That is one hairy integral!

siddarth95
 2 years ago
Best ResponseYou've already chosen the best response.0have you tried considering y^(1/3) as u ?

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.0I don't think you can use usub, since you don't have a du to substitute. But, I think since the integral is from 0<y<1 so it might be easier to just use the bounds given to evaluate. In theory, I think you can use series to solve this.

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.0i would use taylor series to solve this problem

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.0Not series to solve the whole integral! Omg.

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.0i used taylor's expansion and i got 0.1644

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.0unless u want to use integration by parts and the Jacobin and polar coordinate,

mathsmind
 2 years ago
Best ResponseYou've already chosen the best response.0to solve this problem

abb0t
 2 years ago
Best ResponseYou've already chosen the best response.0Well, depending on the course this is being taught in, which is probably a Calc BC (II) course, I would suggest parts. However, if this was for ODE, then I might suggest using poolar coordinates or series expansion.
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