Вычислите интеграл: \int_{-1}^{1} 6x^2 dx

Для начала разберем пример из задания: $\int_{-1}^{1} 6x^2 dx = [2x^3]_{-1}^{1} = 2(1)^3 - 2(-1)^3 = 2 - (-2) = 4$. Вот 30 подобных задач на вычисление определенного интеграла для тренировки: | № | Задание | Ответ | |---|---|---| | 1 | $\int_{0}^{1} 3x^2 dx$ | 1 | | 2 | $\int_{0}^{2} 3x^2 dx$ | 8 | | 3 | $\int_{-1}^{2} 3x^2 dx$ | 9 | | 4 | $\int_{1}^{3} 2x dx$ | 8 | | 5 | $\int_{-2}^{2} x^3 dx$ | 0 | | 6 | $\int_{0}^{1} 4x^3 dx$ | 1 | | 7 | $\int_{1}^{2} 4x^3 dx$ | 15 | | 8 | $\int_{0}^{3} 2x dx$ | 9 | | 9 | $\int_{1}^{4} 2x dx$ | 15 | | 10 | $\int_{-1}^{1} 3x^2 dx$ | 2 | | 11 | $\int_{0}^{1} 5x^4 dx$ | 1 | | 12 | $\int_{-1}^{1} 5x^4 dx$ | 2 | | 13 | $\int_{1}^{2} 6x^2 dx$ | 14 | | 14 | $\int_{0}^{2} x dx$ | 2 | | 15 | $\int_{-1}^{0} x dx$ | -0.5 | | 16 | $\int_{0}^{1} (2x+1) dx$ | 2 | | 17 | $\int_{1}^{2} (2x+1) dx$ | 4 | | 18 | $\int_{0}^{1} (3x^2+2) dx$ | 3 | | 19 | $\int_{-1}^{1} x^5 dx$ | 0 | | 20 | $\int_{0}^{2} 3x^2 dx$ | 8 | | 21 | $\int_{1}^{3} 4x^3 dx$ | 80 | | 22 | $\int_{0}^{1} x^4 dx$ | 0.2 | | 23 | $\int_{-2}^{0} x^2 dx$ | 2.67 | | 24 | $\int_{0}^{3} x^2 dx$ | 9 | | 25 | $\int_{1}^{2} 5x^4 dx$ | 31 | | 26 | $\int_{0}^{2} (x^2+x) dx$ | 4.67 | | 27 | $\int_{-1}^{1} (x^2-1) dx$ | -1.33 | | 28 | $\int_{0}^{1} 6x^5 dx$ | 1 | | 29 | $\int_{1}^{2} 3x^2 dx$ | 7 | | 30 | $\int_{-2}^{1} x^2 dx$ | 3 |