Question

Вычислите интегралы....................

Answer 1

$\int\limits^0_{-1} { \frac{(1-x) ^{4} }{7} } \, dx=- \int\limits^0_{-1} { \frac{(1-x) ^{4} }{7} } \, d(1-x)= =-\frac{(1-x) ^{5} }{5\cdot 7}| _{-1} ^{0} = \\ =- \frac{1}{35}((1-0)^{5} -(1-(-1)) ^{5}) = -\frac{1}{35}(1-2 ^{5} )= \frac{31}{35}$