## ksmith197 Group Title 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? 2 years ago 2 years ago

1. ksmith197 Group Title

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

2. ksmith197 Group Title

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

3. ksmith197 Group Title

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

4. amistre64 Group Title

i think you are confusing a few things

5. amistre64 Group Title

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

6. ksmith197 Group Title

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 Group Title

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 Group Title

oh, i wrote it for the practice:)

9. ksmith197 Group Title

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 Group Title

:) heh

11. amistre64 Group Title

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

12. No-data Group Title

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

13. ksmith197 Group Title

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 Group Title

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

15. ksmith197 Group Title

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

16. TuringTest Group Title

no

17. TuringTest Group Title

$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 Group Title

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 Group Title

Don't worry.

20. TuringTest Group Title

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 Group Title

thta's some crazy cartesian-polar hybrid

22. ksmith197 Group Title

hahaha

23. amistre64 Group Title

but its good to see you thinking outside the mathical box

24. ksmith197 Group Title

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

25. ksmith197 Group Title

thank you all for the help!

26. TuringTest Group Title

welcome :)