Question

Помогите решить плиз срочно !!!!!!!!!!!!

Answer 1

$\int_{2\sqrt2}^4 x\sqrt{x^2-7}dx=[t=x^2-7,dt=2xdx,t_1=4\cdot 2-7=1,\\\\t_2=4^2-7=9]=\int _1^9\sqrt{t}\frac{dt}{2}=\frac{1}{2}\cdot \frac {t^{\frac{3}{2}}}{\frac{3}{2}}|_1^9=\frac{1}{3}(\sqrt{9^3}-1)=\frac{1}{3}\cdot (3^3-1)=\\\\=9-\frac{1}{3}=8\frac{2}{3}\\\\\int 5sin\frac{x}{2}dx=-5\cdot 2\cdot cos\frac{x}{2}+C$