Задача 72126 ...
Условие
r = a*(2-cosα)
математика ВУЗ
71
Решение
★
[m]S= \frac{1}{2} ∫ ^{2π}_{0}(a(2-cos θ ))^2d θ =2\cdot\frac{1}{2}\cdot a^2 ∫ ^{π}_{0}(2-cos θ )^2d θ =a^2∫ ^{π}_{0}(4-4cos θ+cos^2 θ)d θ =a^2∫ ^{π}_{0}(4-4cos θ+\frac{1+cos 2θ}{2})d θ =[/m]
[m]=a^2∫ ^{π}_{0}(4+\frac{1}{2}-4cos θ+\frac{1}{2}cos 2θ)d θ =a^2(\frac{9}{2} θ -4sin θ+\frac{1}{4}sin2 θ)|^{π}_{0} =\frac{9}{2}a^2π[/m]
