急問附加數問題

2008-01-15 6:41 am
i = I sin t
where I is a constant. Find the root mean square value of the current over the interval 0<2rad. given that the [r.m.s(f(x))]^2 = 1/(b-a) ∫[f(x)]^2 dx

回答 (1)

2008-01-15 7:25 am
✔ 最佳答案
you have the formula ...... simply sub
b=2
a=0
f(x) = l sin(x)

I guess your problem is how to integrate [sin(x)]^2 ...
Here you have to lower the degree by using cos(2x) = 1 - 2 [sin(x)]^2
∫[sin(x)]^2 dx
=(1/2) ∫1 - cos(2x) dx
=(1/2) [ x - (1/2) sin(2x)] + C

Thus, the root mean square value
= (1 / 2) (1/2) [ 2 - (1/2)sin(4)] (l^2)
= (1/8) [ 4 - sin(4)] (l^2)


收錄日期: 2021-04-29 19:46:12
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080114000051KK04310

檢視 Wayback Machine 備份