Объяснение:
ДАНО
Y= -x² +6x + 5
Y = x - 1
S = ? - площадь
РЕШЕНИЕ
Пределы интегрирования находим решив уравнение:
- x² + 6x+ 5 = x - 1
- x² + 5x - 4 = 0
Корни уравнения: a = 4, b = 1
Площадь - интеграл разности функции, разность функций запишем в обратном порядке.
S= \int\limits^4_1 {4 -5x+x^2} \, dx= \frac{4x}{1}- \frac{5x^2}{2}+ \frac{x^3}{3} < br / > S=1∫44−5x+x2dx=14x−25x2+3x3<br/>
Вычисляем при а =4 и b =1
S(4)= 16-40 + 21 1/3 = -2 2/3
S(1) = 4 - 2.5 + 1/3 = 1 5/6
И окончательно площадь - разность интегралов.
S = S(1)- S(4) = 1.833 - (-2.667) = 4.5 - площадь - ОТВЕТ
ЖЕДАЛЙАШОВАПРЫГНРМ ВППЦКП
Объяснение:
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