## ksmith197 3 years ago Easy calculus question: if you had something like say a double integral integral[integral (x^2+y^2)/(xy) dy]dx why can't you set x^2 + y^2 = 1?

1. ksmith197

using the cos^2x + sin^2y identity

2. ksmith197

$\int\limits_{1}^{4}\int\limits_{1}^{2}(x^2+y^2)/xy)dydx$

3. ksmith197

why can't the x^2 + y^2 be set = 1

4. amistre64

i think you are confusing a few things

5. amistre64

$\int\int \frac{x^2+y^2}{xy} dy.dx$ $\int\int \frac{x^2}{xy}+\frac{y^2}{xy} dy.dx$ $\int\int \frac{x}{y}+\frac{y}{x} dy.dx$ $\int\int xln(y)+\frac{y^2}{2x} \ dx$etc... if that equates to your idea, then try it out

6. ksmith197

ah sorry didn't mean to make you write all of that out that's actually what the original equation was, i just moved evertying around to try something out

7. ksmith197

was just kinda wondering when you can or can't use the x^2+y^2 = cos[x]^2 + sin[y]^2 = 1 identities

8. amistre64

oh, i wrote it for the practice:)

9. ksmith197

just figured that since we are using double integrals, they are equations with x and y, so i was thinking you could use identities to maybe simplify things

10. ksmith197

:) heh

11. amistre64

(..)^2 is not generally equativalent to the function trig^2(...)

12. No-data

You can use that identity to simplify integrals but you have to be carefull.

13. ksmith197

yeah, the integral didn't come out right in mathematica. Or, could you use it but you have to change the limits of integration?

14. No-data

$x^2+y^2\neq \cos^2x+\sin^2x$

15. ksmith197

ah right but x^2/r^2 + y^2/r^2 = cos[x]^2 + sin[y]^2 = r^2 right?

16. TuringTest

no

17. TuringTest

$x=r\cos\theta$$y=r\sin\theta$$x^2+y^2=r^2\cos^2\theta+r^2\sin^2\theta=r^2$I'm not sure what you are trying to get out of that

18. ksmith197

er yeah, sorry messed that up. it would still work out though right?? because x^2/1 + y^2/1 = (1)^2 cos^2 + sin^2 = 1^2 blehhh i think i'm mixing this all up

19. No-data

Don't worry.

20. TuringTest

you are thinking something like$x^2+y^2=r^2\implies{x^2+y^2\over r^2}=1$perhaps? That would totally screw up your coordinate system though, to put that in the integral

21. TuringTest

thta's some crazy cartesian-polar hybrid

22. ksmith197

hahaha

23. amistre64

but its good to see you thinking outside the mathical box

24. ksmith197

ah i haven't read the chapter on polar stuff yet, so maybe i'll remedy things in the coming week :)

25. ksmith197

thank you all for the help!

26. TuringTest

welcome :)