вычислить интегралы: 1) int (5-4x) от -2 до 1, ответ 21 2) int (6x^2-2x+5) от 0 до 2 3)...

Question

вычислить интегралы:

1) int (5-4x) от -2 до 1, ответ 21

2) int (6x^2-2x+5) от 0 до 2

3) int sinx*dx от пи/3 до 2пи/3

4) int (4x^3 + 6x)dx от -2 до 1

Answer 1

  1                                        1

 ∫ (5 - 4*x) dx = (5*x - 2*x²) I     = (5 * 1 - 2 * 1²) - (5*(-2) - 2 * (-2)²) = 3 - (-18) = 21

-2                                        -2

 2                                                     2

 ∫ (6*x² - 2*x + 5) = (2*x³ - x² + 5*x) I    = (2 * 2³ - 2² + 5 * 2) - 0 = 16 - 4 + 10 = 22

 0                                                    0

2*π/3                         2*π/3

  ∫    cos x dx = sin x I             = sin 2*π/3 - sin π/3 = √ 3 / 2 - √ 3 / 2 = 0

π/3                            π/3 

 1                                             1

 ∫ (4*x³ + 6*x) dx = (x⁴ + 3*x²) I     = (1⁴ + 3*1²) - ((-2)⁴ + 3*(-2)²) = (1 + 3) - (16 + 12) =

-2                                            -2  

= 4 - 28 = -24