Thread: 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

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 . 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 to 2. Thus .