Question

помогите решить интегралы.

Answer 1

Ответ:

$∫ {x}^{4} dx = \frac{ {x}^{5} }{5} + c \\ \frac{ {2}^{5} }{5} - \frac{ {( - 1)}^{4} }{5} = \frac{32 - 1}{5} = \frac{31}{5}$

$∫ {x}^{ - \frac{1}{2} } dx = \frac{ {x}^{ \frac{1}{2} } }{ \frac{1}{2} } + c = 2 \sqrt{x} + c \\ 2 \sqrt{9} - 2 \sqrt{4} = 6 - 4 = 2$

$∫ \cos(x) dx = \sin(x) + c \\ \sin( \frac{\pi}{2} ) - \sin( - \frac{\pi}{2} ) = 1 - ( - 1) = 2$

$∫ \frac{dx}{ { \sin(x) }^{2} } = - ctg(x) + c$

$- ctg( \frac{\pi}{2} ) + ctg( \frac{\pi}{4}) = 0 + 1 = 1$