Integrate x+y where the region is enclosed by y= 3 - x2 and y= 2x by polar parameterization (please only use Polar parameterization?

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I presume you mean y= 3- x^2. The line y= 2x intersects that where 3- x^2= 2x or x^2+ 2x- 3= (x-1)(x+ 3)=0. That is, the graphs intersect at (1, 2) and (-3, -6). In polar coordinates those correspond to \(\displaystyle tan(\theta)= 2\) which has two values in \(\displaystyle -\pi\) to \(\displaystyle \pi\). Integrate \(\displaystyle (r sin(\theta)+r cos(\theta))r drd\theta= (sin(\theta)+ cos(\theta))r^2 drd\theta\) from the negative value to the positive value.
 
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