1.
1) -ctgx| = -ctgπ/2 - (-ctgπ/4) = 0+1=1
2)x-x в -1-ой/-1=x - x в -1 степени = (2+1/2) - (1 + 1) = 2,5 - 2 = 0,5
2.
Sф=∫₀² x³dx=x⁴/4|₀² = 2⁴/4 - 0⁴/4= 4
3. F(x)= 4x⁴/4 - 2x²/2 +3x = x⁴ - x² +3x + с
-2 = 1⁴ -1₃ +3·1 +с
-2 = 3+
с=-5
Ответ: F(x)= x⁴ - x² +3 - 5
4.
1) 1/3·3 sin3x + 1/2·2(-cosx/2)= sin3x-cosx/2 = (sin 3-π/2 - sin 0) - (cosπ/2/2 - cos0) =( -1 - 0) - √2/2-1= -1 - √2/2 +1 = -√2/2
2) 3/2 ·(3x + 4) в степени - 1/2 - x = 3/2 ·1/2((3x + 4) в степени - 1/2) / 1/2 - x²/2= √3x +4 - x²/2 =
(√3·4+4 - 4²/2) - (√3·(-1) +4 - (-1)²/2 = (4-8) - (1-1/2)= -4 -1/2=-4.5