3sqrt(2)acos φ =3asin φ ⇒
tg φ =sqrt(2)
φ =arctg(sqrt(2))
[m] S= ∫_{0} ^{arctg\sqrt{2}}\frac{1}{2}(3asin θ )^2d θ +∫_{arctg\sqrt{2}}^{\frac{π}{2}}\frac{1}{2}(3\sqrt{2}acos θ )^2d θ =[/m]
[m]=\frac{9a^2}{2}∫_{0} ^{arctg\sqrt{2}}sin^2 θ d θ +9a^2∫_{arctg\sqrt{2}}^{\frac{π}{2}}cos^2 θ d θ =[/m]
понижаем степень:
[m]=\frac{9a^2}{2}∫_{0} ^{arctg\sqrt{2}}\frac{1-cos2 θ}{2} d θ +9a^2∫_{arctg\sqrt{2}}^{\frac{π}{2}}\frac{1+cos2 θ}{2} d θ =[/m]
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