Question

Помогите пожалуйста 10 .

Answer 1

₋₁∫⁰(x⁵*(1-x⁶)⁷dx
(1-x⁶)=t
dt=-6*x⁵dx
x⁵dx=-dt/6  ⇒
₋₁∫⁰(t⁷*(-dt/6)=(-1/6)*₋₁∫⁰t⁷dt=(-1/6)*(t⁸/8) ₋₁|⁰=-t⁸/48 ₋₁|⁰=-(1-x⁶)⁸/48 ₋₁|⁰=
=-(1-0⁶)⁸/48-(-(1-(-1)⁶)⁸/48=-1/48-0=-1/48.
Ответ: -1/48.