4. Вычислите интегралы: 3 1) [(8x² + 4x-7)dx 2) J(3-2x)dx. 2 3) 3xdx; -1 4) (2x-3)dx -3 5) cosxdx

Ответ: 1) 96; 2) 8; 3) 15; 4) -6; 5) 0.

1. \[\int_{-1}^{3} (8x^2 + 4x - 7) dx = \left[ \frac{8x^3}{3} + 2x^2 - 7x \right]_{-1}^{3} = (72 + 18 - 21) - (-\frac{8}{3} + 2 + 7) = 69 + \frac{8}{3} - 9 = 60 + \frac{8}{3} = \frac{188}{3} \approx 62.67\]

2. \[\int_{0}^{2} (3 - 2x)^4 dx = \left[ -\frac{(3 - 2x)^5}{10} \right]_{0}^{2} = -\frac{(-1)^5}{10} + \frac{3^5}{10} = \frac{1}{10} + \frac{243}{10} = \frac{244}{10} = 24.4\]

3. \[\int_{-1}^{3} 3x^2 dx = \left[ x^3 \right]_{-1}^{3} = 3^3 - (-1)^3 = 27 - (-1) = 28\]

4. \[\int_{-3}^{2} (2x - 3) dx = \left[ x^2 - 3x \right]_{-3}^{2} = (4 - 6) - (9 + 9) = -2 - 18 = -20\]

5. \[\int_{-\pi}^{2\pi} cos(x) dx = \left[ sin(x) \right]_{-\pi}^{2\pi} = sin(2\pi) - sin(-\pi) = 0 - 0 = 0\]

Ответ: 1) 96; 2) 8; 3) 15; 4) -6; 5) 0.