Question

Evaluate integral by converting to polar coordinates.

Answer 1

Evaluate the iterated integral by converting to polar coordinates.
\[\int\limits_{0}^{2}\int\limits_{0}^{\sqrt{2x-x^2}}\sqrt{x^2 +y^2} dy dx\]

Answer 2

Do it! \(r = \sqrt{x^{2} + y^{2}}\) and \(x = r\cos(\theta)\)

Answer 3

hi we got 0 to pi/2 for limits of theta

Answer 4

i already know about it i'm stuck on getting Radius

Answer 5

i got x^2 + y^2 = 2x therefore R=sqrt(2x).... how do i draw this.?

Answer 6

You should recognize \(x^{2} + y^{2} = 2x\).

\(x^{2} - 2x + y^{2} = 0\)

\(x^{2} - 2x + 1 + y^{2} = 1\)

\((x-1)^{2} + y^{2} = 1\)

Is it looking more familiar, yet?

Answer 7

so the center of circle is (1,0) and limits of radius => 0 to 1 ?