вправа 14.3 гдз 11 клас алгебра Істер 2019
Вправа 14.3
Обчисліть інтеграл:
Умова:
Відповідь ГДЗ:
1 1
✔ 1) ∫ х4dx = х5/5 | = 15/4 - 05/5 = 1/5;
0 0
2 2
✔ 2) ∫ 4dx = 4х | =
-1 -1
= 4 • 2 - 4 • (-1) = 8 + 4 = 12;
π/2 π/2
✔ 3) ∫ sindx = -cosх | =
π/4 π/4
= -cos π/2 + cos π/4 =
= 0 + √2/2 = √2/2;
π/2 π/2
✔ 4) ∫ dx/cos2х = tgх | =
0 0
= tg π/4 - tg0 = 1 - 0 = 1;
2 2
✔ 5) ∫ eхdx = ex | = е2 - е0 = е2 - 1;
0 0
-1 -1
✔ 6) ∫ dx/x = ln |x| | = ln|-1| - ln|-2| =
-2 -2
= ln1 - ln2 = 0 - ln2 = -ln2.
✔ 1) ∫ х4dx = х5/5 | = 15/4 - 05/5 = 1/5;
0 0
2 2
✔ 2) ∫ 4dx = 4х | =
-1 -1
= 4 • 2 - 4 • (-1) = 8 + 4 = 12;
π/2 π/2
✔ 3) ∫ sindx = -cosх | =
π/4 π/4
= -cos π/2 + cos π/4 =
= 0 + √2/2 = √2/2;
π/2 π/2
✔ 4) ∫ dx/cos2х = tgх | =
0 0
= tg π/4 - tg0 = 1 - 0 = 1;
2 2
✔ 5) ∫ eхdx = ex | = е2 - е0 = е2 - 1;
0 0
-1 -1
✔ 6) ∫ dx/x = ln |x| | = ln|-1| - ln|-2| =
-2 -2
= ln1 - ln2 = 0 - ln2 = -ln2.