Вычислите (определенный интеграл):
[tex] \int\limits^1_{-1} {(0,25x+3)^3} \, dx [/tex]
[tex] \int\limits^1_{-1} {(0,25x+3)^3} \, dx [/tex]
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4*интеграл (0,25x + 3)³d(0,25x + 3) =
= 4*[(0,25x + 3)⁴ / 4] = (0,25x + 3)⁴
подставляем пределы интегрирования
(0,25*1 + 3)⁴ - (0,25*(-1) + 3)⁴ = 3,25⁴ - 2,75⁴ =
(3,25²)² - (2,75²)² = (3,25² - 2,75²)*(3,25² + 2,75²) =
= (3,25 - 2,75)*(3,25 + 2,75)*(3,25² + 2,75²) =
= 0,5*6*(10,5625 + 7,5625) = 3 * 18,125 = 54,375