1006 1) ∫(2x-3)dx; 2) ∫(5-4x)dx; 3) ∫(1-3x^2)dx; 4) ∫(x^2+1)dx; 5) ∫(3x^2-4x+5)dx. 1007 1) ∫(x-3√x)dx; 2) ∫(2x-3/√x)dx; 3) ∫e^2xdx; 4) ∫2e^2xdx.

Для решения задач используем формулу Ньютона-Лейбница: $\int_a^b f(x)dx = F(b) - F(a)$, где $F(x)$ — первообразная функции $f(x)$. **Задание 1006** 1) $\int_{-3}^{2} (2x - 3) dx = [x^2 - 3x]_{-3}^{2} = (2^2 - 3 \cdot 2) - ((-3)^2 - 3 \cdot (-3)) = (4 - 6) - (9 + 9) = -2 - 18 = -20$. 2) $\int_{-2}^{-1} (5 - 4x) dx = [5x - 2x^2]_{-2}^{-1} = (5(-1) - 2(-1)^2) - (5(-2) - 2(-2)^2) = (-5 - 2) - (-10 - 8) = -7 - (-18) = 11$. 3) $\int_{-1}^{2} (1 - 3x^2) dx = [x - x^3]_{-1}^{2} = (2 - 2^3) - ((-1) - (-1)^3) = (2 - 8) - (-1 + 1) = -6 - 0 = -6$. 4) $\int_{-1}^{1} (x^2 + 1) dx = [\frac{x^3}{3} + x]_{-1}^{1} = (\frac{1^3}{3} + 1) - (\frac{(-1)^3}{3} + (-1)) = (\frac{1}{3} + 1) - (-\frac{1}{3} - 1) = \frac{4}{3} + \frac{4}{3} = \frac{8}{3} = 2\frac{2}{3}$. 5) $\int_{0}^{2} (3x^2 - 4x + 5) dx = [x^3 - 2x^2 + 5x]_0^2 = (2^3 - 2(2^2) + 5(2)) - 0 = (8 - 8 + 10) = 10$. **Задание 1007** 1) $\int_{0}^{4} (x - 3\sqrt{x}) dx = \int_{0}^{4} (x - 3x^{1/2}) dx = [\frac{x^2}{2} - 3 \cdot \frac{x^{3/2}}{3/2}]_0^4 = [\frac{x^2}{2} - 2x\sqrt{x}]_0^4 = (\frac{16}{2} - 2 \cdot 4 \cdot 2) - 0 = 8 - 16 = -8$. 2) $\int_{1}^{9} (2x - \frac{3}{\sqrt{x}}) dx = \int_{1}^{9} (2x - 3x^{-1/2}) dx = [x^2 - 3 \cdot \frac{x^{1/2}}{1/2}]_1^9 = [x^2 - 6\sqrt{x}]_1^9 = (81 - 6 \cdot 3) - (1 - 6) = (81 - 18) - (-5) = 63 + 5 = 68$. 3) $\int_{0}^{2} e^{2x} dx = [\frac{1}{2}e^{2x}]_0^2 = \frac{1}{2}e^4 - \frac{1}{2}e^0 = \frac{e^4 - 1}{2}$. 4) $\int_{1}^{2} 2e^{2x} dx = [e^{2x}]_1^2 = e^4 - e^2$.