1) f(x) = sin x + cos x; M(pi/2; 14) F(x) = Int f(x) dx = Int (sin x + cos x) dx = -cos x + sin x + C F(pi/2) = -cos(pi/2) + sin(pi/2) + C = -0 + 1 + C = 14 C = 13 F(x) = sin x - cos x + 13
2) a) Int 5(2x^2-3)^2 dx = 5*Int (4x^4 - 12x^2 + 9) dx = = 5*(4x^5/5 - 12x^3/3 + 9x) + C = 4x^5 - 20x^3 + 45x + C
b) Int(0;3) (x^2 + 4x - 1) dx = (x^3/3 + 2x^2 - x)|(0;3) = = 27/3 + 2*9 - 3 - (0 + 0 - 0) = 9 + 18 - 3 = 24 Дальше сам, тут все просто
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1) f(x) = sin x + cos x; M(pi/2; 14)F(x) = Int f(x) dx = Int (sin x + cos x) dx = -cos x + sin x + C
F(pi/2) = -cos(pi/2) + sin(pi/2) + C = -0 + 1 + C = 14
C = 13
F(x) = sin x - cos x + 13
2) a) Int 5(2x^2-3)^2 dx = 5*Int (4x^4 - 12x^2 + 9) dx =
= 5*(4x^5/5 - 12x^3/3 + 9x) + C = 4x^5 - 20x^3 + 45x + C
b) Int(0;3) (x^2 + 4x - 1) dx = (x^3/3 + 2x^2 - x)|(0;3) =
= 27/3 + 2*9 - 3 - (0 + 0 - 0) = 9 + 18 - 3 = 24
Дальше сам, тут все просто