Объяснение:
ρ=2a*(1+cosφ) 0<φ<2π
S=2*(1/2)*₀∫2π(ρ²)dφ=4a²/2*₀∫2π(1+cosφ)²dφ=
=2a²*₀∫2π(2a*(1+cosφ))²dφ=
=2a²*₀∫2π(1+2*cosφ+cos²φ)=
=2a²*₀∫2π(1+2*cosφ+(1+cos(2φ)/2)=
=2a²*₀∫2π(1+2*cosφ+(1/2)+(cos(2φ)/2))=
2a²*(₀∫2π((3/2)(dφ))+₀∫2π(2*cosφ)dφ+₀∫2π(cos²φ)dφ)=
=2a²*((3/2)*φ+2*sinφ ₀|2π+₀∫2π(cos(2φ)/2))=
=2a²*(3*2π/2)+2a²₀∫2π(cos(2φ)dφ=
=6a²π+2a²*sin(2φ)/4 ₀|2π=6a²π+2a²*0/4=6a²π+0=6πa².
