| 1 | ||
∫sin(ωt)sin(ωt)dt=− | cos(ωt)sin(ωt)+∫cos2(ωt)dt | |
| ω |
| 1 | ||
∫sin2(ωt)dt=− | cos(ωt)sin(ωt)+∫(1−sin2(ωt))dt | |
| ω |
| 1 | ||
∫sin2(ωt)dt=− | cos(ωt)sin(ωt)+∫dt−∫sin2(ωt)dt | |
| ω |
| 1 | ||
2∫sin2(ωt)dt=− | cos(ωt)sin(ωt)+t+C1 | |
| ω |
| 1 | 1 | |||
∫sin2(ωt)dt=− | cos(ωt)sin(ωt)+ | t+C | ||
| 2ω | 2 |
| 1 | 1 | 1 | 1 | |||||
=− | cos(ωT)sin(ωT)+ | T−(− | cos(ω0)sin(ω0)+ | 0) | ||||
| 2ω | 2 | 2ω | 2 |
| 1 | 1 | |||
=− | cos(ωT)sin(ωT)+ | T | ||
| 2ω | 2 |