# Thread: pplication of double integrals

1. ## pplication of double integrals

i need help with this.

evaluate : Double integral x dA by changing the polr coordinates, where D is the region in the pfirst quadrant that lies between the circles x^2+y^2=4 and x^2+y^2=2x Thank you

2. Originally Posted by fearless901
i need help with this.

evaluate : Double integral x dA by changing the polar coordinates, where D is the region in the first quadrant that lies between the circles x^2+y^2=4 and x^2+y^2=2x Thank you
The first circle is centred at the origin and has radius 2. Complete the square for the other circle to write it as $\displaystyle (x-1)^2+y^2=1$. So it has radius 1 and is centred at (1,0). Now draw a diagram. You should be able to see from the diagram that for a given value of θ (between 0 and π/2), the region between the two circles corresponds to r going from $\displaystyle 2\cos\theta$ to 2. Thus $\displaystyle \iint_Dx\,dA = \int_0^{\pi/2}\!\!\int_{2\cos\theta}^2r\cos\theta\,rdrd\theta$.