Question

Ребята Решите Подпишусь и лайкну. Заранее

Answer 1

1.

$a)F(x) = \int\limits( - 10 \sin(x)) dx = \\ = - ( - 10 \cos(x)) +c = 10 \cos(x) + c$

$b)F(x) = \int\limits \frac{5}{6} \cos(x)dx = \frac{5}{6} \sin(x) + C \\$

в)

$F(x) = \int\limits(4 {x}^{5} + 3 {x}^{2} + 5x)dx = \\ = \frac{4 {x}^{6} }{6} + \frac{3 {x}^{3} }{3} + \frac{5 {x}^{2} }{2} + c= \\ = \frac{2 {x}^{6} }{3} + {x}^{3} + \frac{5 {x}^{2} }{2} + C$

2.

а)

$F(x) = \int\limits \cos( \frac{3x}{4} ) dx = \\ = \frac{3}{4}\int\limits \cos( \frac{3x}{4} ) d( \frac{3x}{4} ) = \frac{3}{4} \sin( \frac{3x}{4} ) + C$

б)

$F(x) = \int\limits \sin(8x) dx = \frac{1}{8} \int\limits \sin(8x) d(8x) = \\ = - \frac{1}{8} \cos(8x) + C$

в)

$F(x) = \int\limits {(7x + 4)}^{4} dx = \\ = \frac{1}{7} \int\limits {(7x + 4)}^{4} d(7x + 4) = \\ = \frac{ {(7x + 4)}^{5} }{35} + C$

г)

$F(x) = \int\limits {e}^{ \frac{3x + 1}{6}} dx = \int\limits {e}^{ \frac{x}{2} + \frac{1}{6} } dx = \\ = 2\int\limits {e}^{ \frac{x}{2} + \frac{1}{6} } d( \frac{x}{2} + \frac{1}{6} ) = \\ = 2 {e}^{ \frac{3x + 1}{6} } + C$

3.

$S(t) = \int\limits \: v(t)dt = \int\limits4 \cos(6t) dt = \\ = 2 \times 2\int\limits \cos(6t) dt = \frac{2}{3} \int\limits6 \cos(6t) dt = \\ = \frac{2}{3} \int\limits \cos(6t) d(6t) = \frac{2}{3} \sin(6t) + C$

при t = 0 и s = 2

$2 = \frac{2}{3} \sin(0) + C \\ C = 2 \\ S(t) = \frac{2}{3} \sin(6t) + 2$