вправа 14.19 гдз 11 клас алгебра Істер 2019
Вправа 14.19
Обчисліть інтеграл:
Умова:
Відповідь ГДЗ:
π/2 π/2
✔ 1) ∫ sin2хdx = (-cos2х) : 2 | =
0 0
(-cos2•π/2) : 2 + (cos2•0) : 2 =
= -cosπ : 2 + cos0 : 2 =
= -(-1) : 2 + 1/2 = 1/2 + 1/2 = 1;
π π
✔ 2) ∫ 2cos х/6 dx = 2 • 6 • sin х/6 | =
0 0
= 12 • sin π/6 - 12sin 0/6 = 12 • 1/2 - 0 = 6;
π/6 π/6
✔ 3) ∫ 6dx : cos22х = 12 • tg2х | =
0 0
= 12tg2 • π/6 - 12tg2•0 =
= 12tg π/3 = 12кор3;
π/6 π/6
✔ 4) ∫ 3dx : sin23х = -9ctg3х | =
π/12 π/12
= -9ctg3 • π/6 + 9ctg3 • π/12 =
= -9ctg π/3 + 9ctg π/4 =
= -9 • √3/3 + 9 • 1 = -3√3 + 9.
✔ 1) ∫ sin2хdx = (-cos2х) : 2 | =
0 0
(-cos2•π/2) : 2 + (cos2•0) : 2 =
= -cosπ : 2 + cos0 : 2 =
= -(-1) : 2 + 1/2 = 1/2 + 1/2 = 1;
π π
✔ 2) ∫ 2cos х/6 dx = 2 • 6 • sin х/6 | =
0 0
= 12 • sin π/6 - 12sin 0/6 = 12 • 1/2 - 0 = 6;
π/6 π/6
✔ 3) ∫ 6dx : cos22х = 12 • tg2х | =
0 0
= 12tg2 • π/6 - 12tg2•0 =
= 12tg π/3 = 12кор3;
π/6 π/6
✔ 4) ∫ 3dx : sin23х = -9ctg3х | =
π/12 π/12
= -9ctg3 • π/6 + 9ctg3 • π/12 =
= -9ctg π/3 + 9ctg π/4 =
= -9 • √3/3 + 9 • 1 = -3√3 + 9.