Polar coordinates. z=xy and 0

Question

Polar coordinates. z=xy and 0<r<pi/2

Should i do it in cilindric coordinates? x=r cos x and y=r sinx?

anonymous · Answer

It looks as though one of your variables is a bit goofed.  My presumption would be that it should be theta that runs from 0 to pi/2.  In that case, x = r cos theta and y = r sin theta.

anonymous · Answer

yes yes... sorry typo

anonymous · Answer

0<r<1

anonymous · Answer

you went trough a integration by parts right?

anonymous · Answer

$$xy= r \sin(\theta ) r \cos(\theta)  = \frac{1}{2} r^2 \sin(2\theta) $$

anonymous · Answer

The jacobian of the plar substitution is r

anonymous · Answer

$$I = \frac{1}{2}\int\limits_{0}^{1} r^3 dr \int\limits_{0}^{\frac{\pi}{2}} \sin (2\theta ) d \theta $$

anonymous · Answer

yesss thats it :P thanks!

anonymous · Answer

ugh im new to this , wheres the good answer button?

anonymous · Answer

$$= \frac{1}{2} \times \frac{1}{4} \times 1 = \frac{1}{8}$$

anonymous · Answer

just to the right of the username

anonymous · Answer

right to ur username theres "group champion" and a gold medal followed by a zero, theres no actual button to click

anonymous · Answer

huh, strange , ahh dw bout it

anonymous · Answer

there is mean to be a blue button right next to the medal thing

anonymous · Answer

nope... im using safari i dont know if thats something to it ...

anonymous · Answer

yup, safari bugged , there you go. thank you again ;)