Question

ПОМОГИТЕ. ОПРЕДЕЛЁННЫЙ ИНТЕГРАЛ

Answer 1

$\int_{1}^{2} \frac{5dx}{ \sqrt{5x - 1} } = \int_{4}^{9} \frac{1}{ \sqrt{t} }dt = \int_{4}^{9} {t}^{ - \frac{1}{2} } dt = \\ 5x - 1 = t, \: dx = \frac{1}{5} dt; \\ x = 1: \: t = 4, \: x = 2:\: t = 9 \\ = 2 \sqrt{t} |_{4}^{9} = 2 \sqrt{9} - 2 \sqrt{4} = 6 - 4 = 2$

Ответ: 2.