вправа 14.11 гдз 11 клас алгебра Істер 2019
Вправа 14.11
Обчисліть інтеграл:
0
1) ∫ 2√х : х dx;
1
8
2) ∫ (х2dx) : (х4/3)
1
0
1) ∫ 2√х : х dx;
1
8
2) ∫ (х2dx) : (х4/3)
1
Умова:
Відповідь ГДЗ:
0
✔ 1) ∫ 2√х : х dx
1
9 9
2 ∫ √х • х-1dx = 2 ∫ х1/2 • х-1dx =
1 1
9 9
= 2 ∫ х1/2-1dx = 2 ∫ х-1/2dx =
1 1
9 9
= (2•х-1/2+1) : (-1/2 + 1) | = (2х1/2) : 1/2 | =
1 1
2 • 2 • х1/2 | = 4х1/2 | = 4 • 91/2 - 4 • 1 =
= 4 • √9 - 4 = 12 - 4 = 8;
8 8
✔ 2) ∫ (х2dx) : (х4/3) = ∫ х2 • х-4/3dx =
1 1
8
= ∫ х2-4/3dx = ∫ х2/3dx =
1
8 8
= (х2/3+1) : (2/3+1) | = х5/3 : 5/3 | =
1 1
8
= 3х5/3 : 5 | = (3•85/3) : 5 - (3•1) : 5 =
1
= (3•23•5/3) : 5 - 3/5 = (3•25) : 5 - 3/5 =
= 96/5 - 3/5 = 93/5 = 18,6.
✔ 1) ∫ 2√х : х dx
1
9 9
2 ∫ √х • х-1dx = 2 ∫ х1/2 • х-1dx =
1 1
9 9
= 2 ∫ х1/2-1dx = 2 ∫ х-1/2dx =
1 1
9 9
= (2•х-1/2+1) : (-1/2 + 1) | = (2х1/2) : 1/2 | =
1 1
2 • 2 • х1/2 | = 4х1/2 | = 4 • 91/2 - 4 • 1 =
= 4 • √9 - 4 = 12 - 4 = 8;
8 8
✔ 2) ∫ (х2dx) : (х4/3) = ∫ х2 • х-4/3dx =
1 1
8
= ∫ х2-4/3dx = ∫ х2/3dx =
1
8 8
= (х2/3+1) : (2/3+1) | = х5/3 : 5/3 | =
1 1
8
= 3х5/3 : 5 | = (3•85/3) : 5 - (3•1) : 5 =
1
= (3•23•5/3) : 5 - 3/5 = (3•25) : 5 - 3/5 =
= 96/5 - 3/5 = 93/5 = 18,6.