求双纽线r^2=4cos2θ区域的面积,用双重积分做

题目

求双纽线r^2=4cos2θ区域的面积,用双重积分做

答案

S=2*∫[-π/4,π/4]dθ∫[0,2√cos2θ]ρdρ
=4∫[-π/4,π/4]cos2θdθ
=2sis2θ|[-π/4,π/4]
=4