6
2
⎛ x2 ⎞ + ⎜ 6x − ⎟ = ⎜ 2 ⎟⎠ 2 −3 −3 −3 ⎝ 2 8 8 2 = + 9 + 36 − 18 − 12 + 2 = 17 + = 19 . 3 3 3 6
2
6
2 ∫ f (x)dx = ∫ x dx + ∫ (6 − x)dx =
⎧ 1 ⎪ б) f ( x ) = ⎨ x ⎪x 3 ⎩ 2
1
1 4
1 4
∫ f (x)dx = ∫ 4
1043. а)
∫
0 < x ≤1
x3 3
;
x >1
2 1 1 x4 dx + ∫ x 3dx = 2 x 1 + 4 x 1 4
16 − x 2 dx =
0
2
= 2 −1+ 4 − 1
1 2 πr = 4π ; б) 4
0
∫
1045. а)
∫
4 − x 2 dx = πr 2 ⋅
0
4
б)
∫
64 − x 2 dx = πr 2 ⋅
−4 3
1046. а)
0
∫
− x 2 − 2x dx =
−1
60 32 + 4 ⋅ 8 sin 60 o = π + 16 3 360 3 5
1
4
∫ x − 1dx = 1⋅ 2 + 4 ⋅ 2 = 8,5 . 0
1047. а) y = 2cos3x − 3sin 2x + 6, y = 0, x = 0, x = π 6
1 2 π πr = . 4 4
45 2 π + 2⋅ = +1; 360 2 2
2 3 x dx = 2 ⋅ + 3 ⋅ = 6,5 ; б) 2 2 −2
∫
1 2 25π . πr = 4 4
25 − x 2 dx =
−5
4 1 1 1044. а) ∫ 4x − x 2 dx= πr 2 = ⋅ 4π=2π ; б) 2 2 0 2
1 3 =4 . 4 4
π ; 6
π
3 ⎛2 ⎞6 ∫ (2cos3x − 3sin 2x + 6)dx = ⎜ sin 3x + cos 2x + 6x ⎟ = 2 ⎝3 ⎠0 0 2 3 1 3 1 = + − − +π= π− . 3 2 2 2 12 π 5π б) y = 2sin 4x + 3cos 2x + 7, y = 0, x = , x = ; 4 4 5π 4
5π
4
4
3 ⎛ 1 ⎞ 4 S = ∫ (2sin 4x + 3cos 2x + 7)dx = ⎜ − cos 4x + sin 2x + 7x ⎟ = 2 2 ⎝ ⎠π π
17