Question

Вычислить площадь фигуры ограниченной линиями

Answer 1

$int_{-3}^{3}(16-x^2-7)mathrm{dx}=9x|_{-3}^{3}-{1over3}x^3|_{-3}^{3}=9(3+3)-{1over3}(27+27)=54+{54over3}=36\ int_{1}^{3}(4x-3-x^2)mathrm{dx}=2x^2|_{1}^{3}-3x|_{1}^{3}-{1over3}x^3|_{1}^{3}=2(9-1)-3(3-1)-{1over3}(27-1)=16-6-{26over3}=10-{26over3}={4over3}\ int_{-3}^{1}(0-x+1)mathrm{dx}+int_{1}^{3}(x-1)mathrm{dx}={1over2}(x-1)^2|_{1}^{3}-{1over2}(1-x)^2|_{-3}^{1}={1over2}(4-0)-{1over2}(0-16)=2+8=10$