## anonymous 3 years ago Integral help, how to approach this?

1. anonymous

$\int\limits_{0}^{1} \sin(y)(e-e^{y^{1/3} })dy$ 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>

2. abb0t

Wow. 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.

3. anonymous

Except that the product of siny and e^y^1/3 is elliptic. Neither of those will differentiate to zero.

4. anonymous

Heh, 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

5. anonymous

That is one hairy integral!

6. anonymous

have you tried considering y^(1/3) as u ?

7. abb0t

I don't think you can use u-sub, 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.

8. anonymous

i would use taylor series to solve this problem

9. abb0t

Not series to solve the whole integral! Omg.

10. anonymous

i used taylor's expansion and i got 0.1644

11. anonymous

unless u want to use integration by parts and the Jacobin and polar coordinate,

12. anonymous

to solve this problem

13. abb0t

Well, 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.