Question

поможіть плиз треба ​

Answer 1

Ответ:

11

$\int\limits^{ 2 } _ { - 1} {x}^{2}dx = \frac{ {x}^{3} }{3} | ^{2} _ { - 1} = \frac{1}{3} ( {2}^{ 3 } - {( - 1)}^{3} ) )= \\ = \frac{1}{3} (8 - ( - 1)) = \frac{1}{3} \times 9 = 3$

12

$\int\limits^{ 2} _ {1}( {x}^{2} - 2x + 3)dx = ( \frac{ {x}^{3} }{3} - \frac{2 {x}^{2} }{2} + 3x) | ^{2} _ {1} = \\ = ( \frac{ {x}^{3} }{3} - {x}^{2} + 3x) | ^{2} _ {1} = \\ = \frac{8}{3} - 4 + 6 - ( \frac{1}{3} - 1 + 3) = \frac{8}{3} + 2 - \frac{1}{3} - 2 = \frac{7}{3}$

17

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