Calculus 3 Setting up double integral in polar coordinate?

pham q

New member
Can some one help me with setting the integral in polar to find the area lies inside the circle x^2 + y^2 = 4 and to the right of the line x = 1

I got the limit of x go from 1 to 2 and y go from -sqrt(3) to sqrt(3)

however I have trouble finding the limit for r and theta
From x and y i tried to derive the limit for r
and this is what i got r go from sec(theta) up to 2
and theta go from -pi/2 to pi/2 (from the picture) =.=
 
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