Question

Помогите решить интегралы

Answer 1

Ответ:

1

$\int\limits^{ 11 } _ {1} {x}^{3}dx = \frac{ {x}^{4} }{4} | ^{ 11} _ {1} = \frac{ {11}^{4} - 1 }{4} = \frac{14640}{4} = 3660$

2

$\int\limits^{ 1 } _ {0} \frac{dx}{1 + {x}^{2} } = arctg(x)| ^{ 1 } _ {0} = \\ = arctg(1) - arctg(0) = \frac{\pi}{4} - 0 = \frac{\pi}{4}$

3

$\int\limits^{ 10 } _ {0}(3 {x}^{2} + 2x + 2)dx = ( \frac{3 {x}^{3} }{3} + \frac{2 {x}^{2} }{2} + 2x) | ^{ 10} _ {0} = \\ = ( {x}^{3} + {x}^{2} + 2x)| ^{ 10 } _ {0} = \\ = 1000 + 100 + 20 - 0 = 1120$