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I need to evaluate the double integral:I from 0 to 3, I from 0 to sqrt(9-y^2),...

I need to evaluate the double integral:I from 0 to 3, I from 0 to sqrt(9-y^2), integrand is Sqrt(1+x^2 + y^2)dxdy. I know I need to convert to polar coordinates: x = rcos theta, y = rsin- theta. The integrand becomes sqrt(1+r^2)?????. I know how to integrate that, but I don’t know how to convert the bounds for the integrals. I think for dtheta, because we go from the x-axis to the y-axis, so we go from 0 to pi/2. Is that the correct reasoning? But how do I calculate the bounds for the integral over r?

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