i'll use x for theta because i don't know how to make the theta symbol

find the area inside the oval limacon r=4+2cos(x)

so i've squared r to get 16 +16cos(x) +4cos(x)^2

factor out a 4 to get 4(4+4cos(x)+cos(x)^2)

then change to 4(4+4cos(x)+(1+cos2x)/2

factor out a 1/2 and integrate, which comes to

2(3x + 2sin(x)+(sin2x)/2

so i think the limits of integration are from 0 to pi. but i'm not getting the correct answer using those. can anyone help me out?