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
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
∫ (4*x³ + 6*x) dx = (x⁴ + 3*x²) I = (1⁴ + 3*1²) - ((-2)⁴ + 3*(-2)²) = (1 + 3) - (16 + 12) =
= 4 - 28 = -24
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Verified answer
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