Question

Вычислите интеграл сверху 4,снизу - 1, 5dx/x^2

Answer 1

$\displaystyle \limits \int _1^4 \dfrac{5dx}{x^2}=5\displaystyle \int \limits_1^4x^{-2} dx=5\left(\dfrac{x^{-2+1}}{-2+1}\right) \Bigg|_1^4=\left(-\dfrac{5}{x}\right)\Bigg|_1^4=-\dfrac{5}{4}+5=\dfrac{15}{4}.$