| 1 + cos2t | ||
Podstaw: x = 2sint i masz całkę: ∫4cos2tdt , teraz wykorzystaj wzór: cos2t = | ||
| 2 |
| −x2 | ||
∫√4−x2dx=x√4−x2−∫ | dx | |
| √4−x2 |
| 4−x2−4 | ||
∫√4−x2dx=x√4−x2− | dx | |
| √4−x2 |
| dx | ||
∫√4−x2dx=x√4−x2−∫√4−x2dx+4∫ | dx | |
| √4−x2 |
| ||||||||
2∫√4−x2dx=x√4−x2+4∫ | dx | |||||||
| √1−(x/2)2 |
| x | ||
2∫√4−x2dx=x√4−x2+4arcsin( | )+C1 | |
| 2 |
| 1 | x | |||
∫√4−x2dx= | x√4−x2+2arcsin( | )+C | ||
| 2 | 2 |