Question

Помогите решить №6,12,13,14,15. Очень срочно . пожалуйста
Даю 80 баллов !

Answer 1

6. а) cosx = - 1/2
x = +- arccos(-1/2) + 2*pi*n
x = +-(pi - pi/3) + 2*pi*n
x = +- 2pi/3 + 2*pi*n

б)
$2 { sin}^{3} x - sinx = 0 \\ sinx(2 { sin}^{2} x - 1) = 0 \\ sinx = 0 \: or \: sin^{2} x = \frac{1}{2} \\ x = \pi \times n \: \: or \: \: \: x = {( - 1)}^{k} \frac{\pi}{6} + \pi \times k$
12. график на скриншоте.
S = int ot -1 do 1 (2x^2+2) = (2x^3/3 + 2x) | ot -1 do 1 = 2/3 - 2*(-1)^3/3 + 2 - 2*(-1) = 2/3 + 2/3 + 4 = 16/3.

13. V = pi* int ot 3 do 4 (4x)^2 dx = pi* int ot 3 do 5 (16x^2) dx = pi* (16x^3/3) | ot 3 do 4 = pi* (16*4^3/3 - 16*3^3/3) = pi* 592/3

14. v = 6t^2 - 3t^3 = s'(t)
s(t) = int (6t^2-3t^3) = 6t^3/3 - 3t^4/4 + C = 2t^3 - 3t^4 + C

15. d^2 = a^2 + b^2 + c^2 = 3a^2 = 3*7^2 = 147
d = sqrt (147) = 7sqrt (3)