Re: [積分] 三角函數積分
※ 引述《carteregg (EGG)》之銘言：
: 求∫(sinx)^2(cosx)^2 dx
: 除了用 1-(cosx)^2 換掉(sinx)^2以外還有別的方法嗎
: 謝謝!!
[1]
2 2 2 2
∫(sin x)(cos x) dx = ∫ ( 1-cos x ) cos x dx
[2]
2 2 2 2
∫(sin x)(cos x) dx = ∫ ( 1-sin x ) sin x dx
[3]
2 2 1 1
∫(sin x)(cos x) dx = ∫ --- ( 1-cos2x ) --- ( 1+cos2x) dx
2 2
1 2
= --- ∫ ( 1 - cos (2x) ) dx
4
1 2
= --- ∫ sin (2x) dx
4
1 1
= --- ∫ --- ( 1 - cos(4x) ) dx
4 2
x sin(4x)
= --- - --------- + k
8 32
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