Question

Вычислить интеграл . Срочно

Answer 1

$large intint_{D}(18x^2y^2+32x^3y^3)mathrm{dxdy}=2int_{0}^{1}x^2mathrm{dx}int_{-sqrt{x}}^{x^3}(9y^2+16xy^3)mathrm{dy}=***\ int_{-sqrt{x}}^{x^3}(9y^2+16xy^3)mathrm{dy}=3y^3|_{-sqrt{x}}^{x^3}+4xy^4|_{-sqrt{x}}^{x^3}=3(x^9+sqrt{x^3})+4x(x^{12}-x^2)=3x^9+3sqrt{x^3}+4x^{13}-4x^3\ ***=2int_{0}^{1}(3x^{11}+3x^2sqrt{x^3}+4x^{15}-4x^5)mathrm{dx}=2int_{0}^{1}(3x^{11}+3sqrt{x^7}+4x^{15}-4x^5)mathrm{dx}={x^{16}+x^{12}over2}|_{0}^{1}+{4(sqrt{x^9}-x^6)over3}|_{0}^{1}={1over2}(1-0+1-0)+{4over3}(1-0-1+0)={1over2}cdot2=1$